Markov Regime Switching of Stochastic Volatility Lévy Model on Approximation Mode
Arthit Intarasit
2013-01-01
Full Text Available This paper deals with financial modeling to describe the behavior of asset returns, through consideration of economic cycles together with the stylized empirical features of asset returns such as fat tails. We propose that asset returns are modeled by a stochastic volatility Lévy process incorporating a regime switching model. Based on the risk-neutral approach, there exists a large set of candidates of martingale measures due to the driving of a stochastic volatility Lévy process in the proposed model which renders the market incomplete in general. We first establish an equivalent martingale measure for the proposed model introduced in risk-neutral version. Regime switching of stochastic volatility Lévy process is employed in an approximation mode for model calibration and the calibration of parameters model done based on EM algorithm. Finally, some empirical results are illustrated via applications to the Bangkok Stock Exchange of Thailand index.
A regime-switching stochastic volatility model for forecasting electricity prices
Exterkate, Peter; Knapik, Oskar
In a recent review paper, Weron (2014) pinpoints several crucial challenges outstanding in the area of electricity price forecasting. This research attempts to address all of them by i) showing the importance of considering fundamental price drivers in modeling, ii) developing new techniques...... for probabilistic (i.e. interval or density) forecasting of electricity prices, iii) introducing an universal technique for model comparison. We propose new regime-switching stochastic volatility model with three regimes (negative jump, normal price, positive jump (spike)) where the transition matrix depends...... on explanatory variables. Bayesian inference is explored in order to obtain predictive densities. The main focus of the paper is on shorttime density forecasting in Nord Pool intraday market. We show that the proposed model outperforms several benchmark models at this task....
Stochastic Functional Differential Equation under Regime Switching
Ling Bai
2012-01-01
Full Text Available We discuss stochastic functional differential equation under regime switching dx(t=f(xt,r(t,tdt+q(r(tx(tdW1(t+σ(r(t|x(t|βx(tdW2(t. We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially stable of this system.
Nonzero-Sum Stochastic Differential Portfolio Games under a Markovian Regime Switching Model
Chaoqun Ma
2015-01-01
Full Text Available We consider a nonzero-sum stochastic differential portfolio game problem in a continuous-time Markov regime switching environment when the price dynamics of the risky assets are governed by a Markov-modulated geometric Brownian motion (GBM. The market parameters, including the bank interest rate and the appreciation and volatility rates of the risky assets, switch over time according to a continuous-time Markov chain. We formulate the nonzero-sum stochastic differential portfolio game problem as two utility maximization problems of the sum process between two investors’ terminal wealth. We derive a pair of regime switching Hamilton-Jacobi-Bellman (HJB equations and two systems of coupled HJB equations at different regimes. We obtain explicit optimal portfolio strategies and Feynman-Kac representations of the two value functions. Furthermore, we solve the system of coupled HJB equations explicitly in a special case where there are only two states in the Markov chain. Finally we provide comparative statics and numerical simulation analysis of optimal portfolio strategies and investigate the impact of regime switching on optimal portfolio strategies.
Selection Criteria in Regime Switching Conditional Volatility Models
Thomas Chuffart
2015-05-01
Full Text Available A large number of nonlinear conditional heteroskedastic models have been proposed in the literature. Model selection is crucial to any statistical data analysis. In this article, we investigate whether the most commonly used selection criteria lead to choice of the right specification in a regime switching framework. We focus on two types of models: the Logistic Smooth Transition GARCH and the Markov-Switching GARCH models. Simulation experiments reveal that information criteria and loss functions can lead to misspecification ; BIC sometimes indicates the wrong regime switching framework. Depending on the Data Generating Process used in the experiments, great care is needed when choosing a criterion.
Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction
Zheng Wu
2013-01-01
Full Text Available This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.
DETECTING REGIME SWITCHES IN THE EUR/RON EXCHANGE RATE VOLATILITY
Radu Alina-Nicoleta
2009-05-01
Full Text Available In the present study we develop and implement a short term exchange rate forecasting methodology using dynamic confidence intervals based on GARCH processes and we analyze whether this methodology can be used to model a regime switch in the volatility of
On the robustness of international portfolio diversification benefits to regime-switching volatility
Flavin, Thomas; Panopoulou, Ekaterini
2009-01-01
We examine if the benefits of international portfolio diversification are robust to time-varying asset return volatility. Since diversified portfolios are subject to common cross-country shocks, we focus on the transmission mechanism of such shocks in the presence of regime-switching volatility. Generally, market linkages are stable with little evidence of increased market interdependence in turbulent periods. Furthermore, risk reduction is consistently delivered for the US investor who holds...
Regime Switching Vine Copula Models for Global Equity and Volatility Indices
Holger Fink
2017-01-01
Full Text Available For nearly every major stock market there exist equity and implied volatility indices. These play important roles within finance: be it as a benchmark, a measure of general uncertainty or a way of investing or hedging. It is well known in the academic literature that correlations and higher moments between different indices tend to vary in time. However, to the best of our knowledge, no one has yet considered a global setup including both equity and implied volatility indices of various continents, and allowing for a changing dependence structure. We aim to close this gap by applying Markov-switching R-vine models to investigate the existence of different, global dependence regimes. In particular, we identify times of “normal” and “abnormal” states within a data set consisting of North-American, European and Asian indices. Our results confirm the existence of joint points in a time at which global regime switching between two different R-vine structures takes place.
Stochastic volatility and stochastic leverage
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Zhao, Yu; Yuan, Sanling; Zhang, Tonghua
2016-08-01
The effect of toxin-producing phytoplankton and environmental stochasticity are interesting problems in marine plankton ecology. In this paper, we develop and analyze a stochastic phytoplankton allelopathy model, which takes both white and colored noises into account. We first prove the existence of the global positive solution of the model. And then by using the stochastic Lyapunov functions, we investigate the positive recurrence and ergodic property of the model, which implies the existence of a stationary distribution of the solution. Moreover, we obtain the mean and variance of the stationary distribution. Our results show that both the two kinds of environmental noises and toxic substances have great impacts on the evolution of the phytoplankton populations. Finally, numerical simulations are carried out to illustrate our theoretical results.
Stochastic volatility selected readings
Shephard, Neil
2005-01-01
Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major issues involved. General Introduction N. Shephard. Part I: Model Building. 1. A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, (P. K. Clark). 2. Financial Returns Modelled by the Product of Two Stochastic Processes: A Study of Daily Sugar Prices, 1961-7, S. J. Taylor. 3. The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices, B. Rosenberg. 4. The Pricing of Options on Assets with Stochastic Volatilities, J. Hull and A. White. 5. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model, F. X. Diebold and M. Nerlove. 6. Multivariate Stochastic Variance Models. 7. Stochastic Autoregressive...
Level-ARCH Short Rate Models with Regime Switching
Christiansen, Charlotte
This paper introduces regime switching volatility into level- ARCH models for the short rates of the US, the UK, and Germany. Once regime switching and level effects are included there are no gains from including ARCH effects. It is of secondary importance exactly how the regime switching...
Equilibrium yield curves under regime switching
García-Verdú, Santiago
2010-01-01
This paper studies how inflation as a macroeconomic indicator affects nominal bond prices. I consider an economy with a representative agent with Epstein- Zin preferences. Regime switching affects the state-space capturing inflation and consumption growth. Thus, the agent is concerned about the intertemporal distribution of risk, which is affected by the persistence of the variables and the regimes. Regime switching allows for structural changes in the volatility of unexpected shocks. To the ...
Todorova, Milena
Essay 1. The paper analyzes the price dynamics of two commodity futures prices---crude oil and natural gas. Some of the latest models of commodity prices are tested here---the two-factor model of Schwartz-Smith (2000), which nests other important models developed earlier. The two-factor model includes a mean-reverting short-term deviation and uncertain equilibrium level to which prices gravitate. The Schwartz-Smith two-factor model is the base case model in the paper. The model parameters of the Schwartz-Smith two-factor model are estimated from traded futures on natural gas and crude oil, using the fixed maturity format I create for futures prices. Analysis of the variance structure of natural gas prices suggests seasonality. The model is estimated on seasonally adjusted data. Model-based seasonality approaches are developed---seasonal dummies and a three-factor model with a stochastic seasonality component of log spot prices. The prediction ability of the various parameterized and non-parameterized versions of models with seasonality is compared in-sample and out-of-sample. The volatility functions model, based on principal components extraction from daily data, with seasonality in short-term volatility, seems to have the best forecasting ability, followed by the two-factor model on Kendall-type deseasonalized data and the seasonal dummies specification. Essay 2. This paper contributes to the extant structural model literature by introducing a time-varying risk-shifting barrier, to model asset substitution, and studying its theoretical and empirical implications on corporate credit spreads. Risk-shifting is expected to affect the default component of corporate spreads, because by switching to a higher level of asset volatility, managers precipitate the onset of distress and endogenously alter the probability of default. I test cross-sectionally whether the risk of volatility regime switching, measured by agency cost, is priced in market corporate spreads. The
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Stochastic Volatility and DSGE Models
Andreasen, Martin Møller
This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...
在模式转换市场与随机利率条件下的投资组合问题%The Portfolio Problems with Regime-switching and Stochastic Interest Rates
梁月; 王子亭; 王晓洁
2011-01-01
Investment problems where an investor can invest in a saving account,stocks with Markov-modulated regime-switching and stochastic interest rates and tries to maximize her/his expected utility of the terminal wealth are studied.The optimal portfolio problem is transformed into optimal control problem,and then is changed into HJB equation and ODEs.At the same time,HJB equation being strictly convex quadratic function on the control of π（the wealth invested in risky asset） is proved.At last,it is proved that the optimal percentage of total wealth θ invested in the risky asset with regime-switching and stochastic interest rates just depends on different market modes parameters.%本文考虑在Markov调制的模式转换市场与随机利率条件下,投资于无风险资产储蓄账户和风险资产股票的组合问题,研究使投资者的终时期望效用最大的最优投资组合。本文将最优投资问题转化为最优控制问题,进而转化为求解HJB方程模型,并直接证明了此HJB方程是关于控制π（投资于风险资产的财富）的严格凹的二次函数,随后转化为求解常微分方程组的问题。最终得到在模式转换市场与随机利率情况下投资于风险资产的财富比例θ只与不同市场模式下的各项参数相关。
CAM Stochastic Volatility Model for Option Pricing
Wanwan Huang
2016-01-01
Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.
Regime switching model for financial data: Empirical risk analysis
Salhi, Khaled; Deaconu, Madalina; Lejay, Antoine; Champagnat, Nicolas; Navet, Nicolas
2016-11-01
This paper constructs a regime switching model for the univariate Value-at-Risk estimation. Extreme value theory (EVT) and hidden Markov models (HMM) are combined to estimate a hybrid model that takes volatility clustering into account. In the first stage, HMM is used to classify data in crisis and steady periods, while in the second stage, EVT is applied to the previously classified data to rub out the delay between regime switching and their detection. This new model is applied to prices of numerous stocks exchanged on NYSE Euronext Paris over the period 2001-2011. We focus on daily returns for which calibration has to be done on a small dataset. The relative performance of the regime switching model is benchmarked against other well-known modeling techniques, such as stable, power laws and GARCH models. The empirical results show that the regime switching model increases predictive performance of financial forecasting according to the number of violations and tail-loss tests. This suggests that the regime switching model is a robust forecasting variant of power laws model while remaining practical to implement the VaR measurement.
Oil and stock market volatility: A multivariate stochastic volatility perspective
Vo, Minh, E-mail: minh.vo@metrostate.edu
2011-09-15
This paper models the volatility of stock and oil futures markets using the multivariate stochastic volatility structure in an attempt to extract information intertwined in both markets for risk prediction. It offers four major findings. First, the stock and oil futures prices are inter-related. Their correlation follows a time-varying dynamic process and tends to increase when the markets are more volatile. Second, conditioned on the past information, the volatility in each market is very persistent, i.e., it varies in a predictable manner. Third, there is inter-market dependence in volatility. Innovations that hit either market can affect the volatility in the other market. In other words, conditioned on the persistence and the past volatility in their respective markets, the past volatility of the stock (oil futures) market also has predictive power over the future volatility of the oil futures (stock) market. Finally, the model produces more accurate Value-at-Risk estimates than other benchmarks commonly used in the financial industry. - Research Highlights: > This paper models the volatility of stock and oil futures markets using the multivariate stochastic volatility model. > The correlation between the two markets follows a time-varying dynamic process which tends to increase when the markets are more volatile. > The volatility in each market is very persistent. > Innovations that hit either market can affect the volatility in the other market. > The model produces more accurate Value-at-Risk estimates than other benchmarks commonly used in the financial industry.
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Some recent developments in stochastic volatility modelling
Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.
2002-01-01
This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...
Bayesian Vector Autoregressions with Stochastic Volatility
Uhlig, H.F.H.V.S.
1996-01-01
This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate.Exact updating formulas are given to the nonlinear filtering of the precision matrix.Estimation of the au
Bayesian Vector Autoregressions with Stochastic Volatility
Uhlig, H.F.H.V.S.
1996-01-01
This paper proposes a Bayesian approach to a vector autoregression with stochastic volatility, where the multiplicative evolution of the precision matrix is driven by a multivariate beta variate.Exact updating formulas are given to the nonlinear filtering of the precision matrix.Estimation of the
Option Pricing when the Regime-Switching Risk is Priced
Tak Kuen Siu; Hailiang Yang
2009-01-01
We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a twostage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.
Portfolio Selection with Jumps under Regime Switching
Lin Zhao
2010-01-01
Full Text Available We investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection is proposed and analyzed for a market consisting of one bank account and multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. A Markov chain modulated diffusion formulation is employed to model the problem.
Have East Asian stock markets calmed down? Evidence from a regime-switching model
Chaudhuri, K.R.; Klaassen, F.
2001-01-01
The 1997-98 East Asian crisis was accompanied by high volatility of East Asian stock returns. This paper examines whether the volatility has already come down to the level of the years before the crisis. We use a regime-switching model to account for possible structural change in the unconditional v
Have East Asian stock markets calmed down? Evidence from a regime-switching model
Chaudhuri, K.R.; Klaassen, F.
2001-01-01
The 1997-98 East Asian crisis was accompanied by high volatility of East Asian stock returns. This paper examines whether the volatility has already come down to the level of the years before the crisis. We use a regime-switching model to account for possible structural change in the unconditional
Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility
van Haastrecht, A.; Lord, R.; Pelsser, A.; Schrager, D.
2009-01-01
We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Sc
Understanding Interest Rate Volatility
Volker, Desi
This thesis is the result of my Ph.D. studies at the Department of Finance of the Copenhagen Business School. It consists of three essays covering topics related to the term structure of interest rates, monetary policy and interest rate volatility. The rst essay, \\Monetary Policy Uncertainty...... and Interest Rates", examines the role of monetary policy uncertainty on the term structure of interest rates. The second essay, \\A Regime-Switching A ne Term Structure Model with Stochastic Volatility" (co-authored with Sebastian Fux), investigates the ability of the class of regime switching models...... with and without stochastic volatility to capture the main stylized features of U.S. interest rates. The third essay, \\Variance Risk Premia in the Interest Rate Swap Market", investigates the time-series and cross-sectional properties of the compensation demanded for holding interest rate variance risk. The essays...
Viscosity methods for multiscale financial models with stochastic volatility
Bardi, Martino; Cesaroni, Annalisa; Ghilli, Daria; Scotti, Andrea
2014-01-01
Parallel session; International audience; Introduction on models Financial models and stochastic volatility, Gaussian or with jumps Fast stochastic volatility Part 1 Control systems with random parameters and multiple scales The Hamilton-Jacobi-Bellman approach to Singular Perturbations I Tools I Assumptions I A convergence result Applications to finance Part 2 Large deviations for small time to maturity: see also Daria Ghilli's poster tomorrow
Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility
Min-Ku Lee
2014-01-01
Full Text Available Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.
Estimation of Stochastic Volatility Models by Nonparametric Filtering
Kanaya, Shin; Kristensen, Dennis
2016-01-01
/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases......A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...
van Haastrecht, A.; Pelsser, A.
2009-01-01
We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal)
The multivariate supOU stochastic volatility model
Barndorff-Nielsen, Ole; Stelzer, Robert
structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations......Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order...
On changes of measure in stochastic volatility models
Bernard Wong
2006-01-01
models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.
On Volatility Induced Stationarity for Stochastic Differential Equations
Albin, J.M.P.; Astrup Jensen, Bjarne; Muszta, Anders;
2006-01-01
This article deals with stochastic differential equations with volatility induced stationarity. We study of theoretical properties of such equations, as well as numerical aspects, together with a detailed study of three examples.......This article deals with stochastic differential equations with volatility induced stationarity. We study of theoretical properties of such equations, as well as numerical aspects, together with a detailed study of three examples....
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut
Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general...... properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic scaling of the amplitude, to stochastic time change and extended subordination of random measures...... and to probability and L\\'{e}vy mixing of volatility/intensity parameters will be developed. Important examples for concrete model specifications within the class of ambit fields are given....
A Jump-Diffusion Model with Stochastic Volatility and Durations
Wei, Wei; Pelletier, Denis
Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price...... jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps....... The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation...
Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility
Mark J. Jensen
2015-01-01
Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance - but still mean reverting - behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic ...
Shao Dian-guo
2016-01-01
In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.
On efficient Bayesian inference for models with stochastic volatility
Griffin, Jim E.; Sakaria, Dhirendra Kumar
2016-01-01
An efficient method for Bayesian inference in stochastic volatility models uses a linear state space representation to define a Gibbs sampler in which the volatilities are jointly updated. This method involves the choice of an offset parameter and we illustrate how its choice can have an important effect on the posterior inference. A Metropolis-Hastings algorithm is developed to robustify this approach to choice of the offset parameter. The method is illustrated on simulated data with known p...
Testing for regime-switching CAPM on Zagreb Stock Exchange
Tihana Škrinjarić
2014-12-01
Full Text Available The standard Capital Asset Pricing Model assumes that a linear relationship exists between the risk (beta and the expected excess return of a stock. However, empirical findings have shown over the years that this relationship varies over time. Stock markets undergo phases of greater and smaller volatility in which beta varies accordingly (undergoes different regimes. Given that the Croatian capital market is still insufficiently investigated, the aim of this paper is to explore the possibility of a non-linear relationship between the stock risk and return. Linear and Markov-switching models (Hamilton 1989 are examined on the Zagreb Stock Exchange based on monthly data on 21 stocks, ranging from January 2005 to December 2013. In that way, investors can use the results based on the best model when making decisions about buying stocks. Since this is one of the first papers on regime-switching on the Croatian capital market, it will hopefully contribute to the existing literature on investing.
Regime switches induced by supply-demand equilibrium: a model for power-price dynamics
Mari, Carlo; Tondini, Daniela
2010-11-01
Regime-switching models can be used to describe stochastic movements of electricity prices in deregulated markets. This paper shows that regime-switching dynamics arise quite naturally in an equilibrium context in which the functional form of the supply curve is described by a two-state Markov process. This mechanism is responsible for random switches between regimes and it allows one to describe the main features of the price-formation process. With the interplay between demand and supply, the proposed methodology can be used to capture shortages in electricity generation, forced outages, and peaks in electricity demand. As an example of application, a two-regime model specification is proposed, and it will be shown that the empirical analysis, performed by estimating using the model on the California power market, offers an interesting agreement with observed data.
Bias-reduced estimation of long memory stochastic volatility
Frederiksen, Per; Nielsen, Morten Ørregaard
We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstation- arity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining...... bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators....
Regime-Switching Risk: To Price or Not to Price?
Tak Kuen Siu
2011-01-01
“normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
The correlation dimension of returns with stochastic volatility
Diks, C.G.H.
2004-01-01
Signs of low-dimensional scaling of correlation integrals of financial returns have often been reported in the literature. In this paper conditions are considered under which correlation integrals of returns generated by stochastic volatility models show scaling. Subject to certain conditions on the
The correlation dimension of returns with stochastic volatility
Diks, C.G.H.
2004-01-01
Signs of low-dimensional scaling of correlation integrals of financial returns have often been reported in the literature. In this paper conditions are considered under which correlation integrals of returns generated by stochastic volatility models show scaling. Subject to certain conditions on the
Estimating Stochastic Volatility Models using Prediction-based Estimating Functions
Lunde, Asger; Brix, Anne Floor
In this paper prediction-based estimating functions (PBEFs), introduced in Sørensen (2000), are reviewed and PBEFs for the Heston (1993) stochastic volatility model are derived. The finite sample performance of the PBEF based estimator is investigated in a Monte Carlo study, and compared to the p......In this paper prediction-based estimating functions (PBEFs), introduced in Sørensen (2000), are reviewed and PBEFs for the Heston (1993) stochastic volatility model are derived. The finite sample performance of the PBEF based estimator is investigated in a Monte Carlo study, and compared...... to the performance of the GMM estimator based on conditional moments of integrated volatility from Bollerslev and Zhou (2002). The case where the observed log-price process is contaminated by i.i.d. market microstructure (MMS) noise is also investigated. First, the impact of MMS noise on the parameter estimates from...
Stochastic volatility of the futures prices of emission allowances: A Bayesian approach
Kim, Jungmu; Park, Yuen Jung; Ryu, Doojin
2017-01-01
Understanding the stochastic nature of the spot volatility of emission allowances is crucial for risk management in emissions markets. In this study, by adopting a stochastic volatility model with or without jumps to represent the dynamics of European Union Allowances (EUA) futures prices, we estimate the daily volatilities and model parameters by using the Markov Chain Monte Carlo method for stochastic volatility (SV), stochastic volatility with return jumps (SVJ) and stochastic volatility with correlated jumps (SVCJ) models. Our empirical results reveal three important features of emissions markets. First, the data presented herein suggest that EUA futures prices exhibit significant stochastic volatility. Second, the leverage effect is noticeable regardless of whether or not jumps are included. Third, the inclusion of jumps has a significant impact on the estimation of the volatility dynamics. Finally, the market becomes very volatile and large jumps occur at the beginning of a new phase. These findings are important for policy makers and regulators.
Option Pricing with Stochastic Volatility and Jump Diffusion Processes
Radu Lupu
2006-05-01
Full Text Available Option pricing by the use of Black Scholes Merton (BSM model is based on the assumption that asset prices have a lognormal distribution. In spite of the use of these models on a large scale, both by practioners and academics, the assumption of lognormality is rejected by the history of returns. The objective of this article is to present the methods that developed after the Black Scholes Merton environment and deals with the option pricing model adjustment to the empirical properties of asset returns. The main models that appeared after BSM allowed for special changes of the returns that materialized in jump-diffusion and stochastic volatility processes. The article presents the foundations of risk neutral options evaluation and the empirical evidence that fed the amendment of the lognormal assumption in the first part and shows the evaluation procedure under the assumption of stock prices following the jump-diffusion process and the stochastic volatility process.
Option Pricing with Stochastic Volatility and Jump Diffusion Processes
Radu Lupu
2006-03-01
Full Text Available Option pricing by the use of Black Scholes Merton (BSM model is based on the assumption that asset prices have a lognormal distribution. In spite of the use of these models on a large scale, both by practioners and academics, the assumption of lognormality is rejected by the history of returns. The objective of this article is to present the methods that developed after the Black Scholes Merton environment and deals with the option pricing model adjustment to the empirical properties of asset returns. The main models that appeared after BSM allowed for special changes of the returns that materialized in jump-diffusion and stochastic volatility processes. The article presents the foundations of risk neutral options evaluation and the empirical evidence that fed the amendment of the lognormal assumption in the first part and shows the evaluation procedure under the assumption of stock prices following the jump-diffusion process and the stochastic volatility process.
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
Jiang, G.J.; van der Sluis, P.J.
2000-01-01
This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the
High order discretization schemes for stochastic volatility models
Jourdain, Benjamin
2009-01-01
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using It\\^o's formula, we get rid, in the asset price dynamics, of the stochastic integral with respect to the Brownian motion driving this SDE. Taking advantage of this structure, we propose - a scheme, based on the Milstein discretization of this SDE, with order one of weak trajectorial convergence for the asset price, - a scheme, based on the Ninomiya-Victoir discretization of this SDE, with order two of weak convergence for the asset price. We also propose a specific scheme with improved convergence properties when the volatility of the asset price is driven by an Orstein-Uhlenbeck process. We confirm the theoretical rates of convergence by numerical experiments and show that our schemes are well adapted to the multilevel Monte Carlo method introduced by Giles [2008a,b].
Trading Strategy with Stochastic Volatility in a Limit Order Book Market
Ching, Wai-Ki; Gu, Jia-Wen; Siu, Tak-Kuen; Yang, Qing-Qing
2016-01-01
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the controlled state process is the dealer's mark-to-market wealth. Dealers in the s...
无
2003-01-01
In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.
Simple approximations for option pricing under mean reversion and stochastic volatility
C.M. Hafner (Christian)
2003-01-01
textabstractThis paper provides simple approximations for evaluating option prices and implied volatilities under stochastic volatility. Simple recursive formulae are derived that can easily be implemented in spreadsheets. The traditional random walk assumption, dominating in the analysis of
Bach, Christian; Christensen, Bent Jesper
We include simultaneously both realized volatility measures based on high-frequency asset returns and implied volatilities backed out of individual traded at the money option prices in a state space approach to the analysis of true underlying volatility. We model integrated volatility as a latent...... fi…rst order Markov process and show that our model is closely related to the CEV and Barndorff-Nielsen & Shephard (2001) models for local volatility. We show that if measurement noise in the observable volatility proxies is not accounted for, then the estimated autoregressive parameter in the latent...... process is downward biased. Implied volatility performs better than any of the alternative realized measures when forecasting future integrated volatility. The results are largely similar across the stock market (S&P 500), bond market (30-year U.S. T-bond), and foreign currency exchange market ($/£ )....
Stochastic Volatility and Option Pricing in Heath-Jarrow-Morton Term Structure Analysis
Christensen, Bent Jesper; Konaris, George; Nicolato, Elisa
We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented.......We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented....
Stochastic Volatility Model and Technical Analysis of Stock Price
Wei LIU; Wei An ZHENG
2011-01-01
In the stock market, some popular technical analysis indicators (e.g. Bollinger Bands, RSI,ROC, ...) are widely used by traders. They use the daily (hourly, weekly, ...) stock prices as samples of certain statistics and use the observed relative frequency to show the validity of those well-knownindicators. However, those samples are not independent, so the classical sample survey theory does not apply. In earlier research, we discussed the law of large numbers related to those observations when one assumes Black-Scholes' stock price model. In this paper, we extend the above results to the more popular stochastic volatility model.
Option pricing with transaction costs and stochastic volatility
Ionut Florescu
2014-07-01
Full Text Available In a realistic market with transaction costs, the option pricing problem is known to lead to solving nonlinear partial differential equations even in the simplest model. The nonlinear term in these partial differential equations (PDE reflects the presence of transaction costs. In this article we consider an underlying general stochastic volatility model. In this case the market is incomplete and the option price is not unique. Under a particular market completion assumption where we use a traded proxy for the volatility, we obtain a non-linear PDE whose solution provides the option price in the presence of transaction costs. This PDE is studied and under suitable regularity conditions, we prove the existence of strong solutions of the problem.
Bayesian Option Pricing Framework with Stochastic Volatility for FX Data
Ying Wang
2016-12-01
Full Text Available The application of stochastic volatility (SV models in the option pricing literature usually assumes that the market has sufficient option data to calibrate the model’s risk-neutral parameters. When option data are insufficient or unavailable, market practitioners must estimate the model from the historical returns of the underlying asset and then transform the resulting model into its risk-neutral equivalent. However, the likelihood function of an SV model can only be expressed in a high-dimensional integration, which makes the estimation a highly challenging task. The Bayesian approach has been the classical way to estimate SV models under the data-generating (physical probability measure, but the transformation from the estimated physical dynamic into its risk-neutral counterpart has not been addressed. Inspired by the generalized autoregressive conditional heteroskedasticity (GARCH option pricing approach by Duan in 1995, we propose an SV model that enables us to simultaneously and conveniently perform Bayesian inference and transformation into risk-neutral dynamics. Our model relaxes the normality assumption on innovations of both return and volatility processes, and our empirical study shows that the estimated option prices generate realistic implied volatility smile shapes. In addition, the volatility premium is almost flat across strike prices, so adding a few option data to the historical time series of the underlying asset can greatly improve the estimation of option prices.
Practical stability and instability of regime-switching diffusions
G.George YIN; Bo ZHANG; Chao ZHU
2008-01-01
This work is devoted to practical stability of a class of regime-switching diffusions.First,the notion of practical stability is introduced.Then,sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument.In addition,easily verifiable conditions on drift and diffusion coefficients are also given.Moreover,examples are supplied for demonstration purposes.
An equity-interest rate hybrid model with stochastic volatility and the interest rate smile
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main
Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility
Christensen, Peter Ove; Larsen, Kasper
and can trade continuously on a finite time interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic counter-cyclical volatility, the resulting equilibrium can display......In an incomplete continuous-time securities market governed by Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and equity premium processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income...... both lower risk-free rates and higher risk premia relative to the Pareto efficient equilibrium in an otherwise identical complete market. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility
Christensen, Peter Ove; Larsen, Kasper
and can trade continuously on a finite time interval in a money market account and a single risky security. Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic counter-cyclical volatility, the resulting equilibrium can display......In an incomplete continuous-time securities market governed by Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and equity premium processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income...... both lower risk-free rates and higher risk premia relative to the Pareto efficient equilibrium in an otherwise identical complete market. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles....
Variational Bayes for Regime-Switching Log-Normal Models
Hui Zhao
2014-07-01
Full Text Available The power of projection using divergence functions is a major theme in information geometry. One version of this is the variational Bayes (VB method. This paper looks at VB in the context of other projection-based methods in information geometry. It also describes how to apply VB to the regime-switching log-normal model and how it provides a computationally fast solution to quantify the uncertainty in the model specification. The results show that the method can recover exactly the model structure, gives the reasonable point estimates and is very computationally efficient. The potential problems of the method in quantifying the parameter uncertainty are discussed.
Pricing Exotic Options under a High-Order Markovian Regime Switching Model
Wai-Ki Ching
2007-01-01
by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM. We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.
Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters
Wen Xu
2016-10-01
Full Text Available Time-varying volatility is common in macroeconomic data and has been incorporated into macroeconomic models in recent work. Dynamic panel data models have become increasingly popular in macroeconomics to study common relationships across countries or regions. This paper estimates dynamic panel data models with stochastic volatility by maximizing an approximate likelihood obtained via Rao-Blackwellized particle filters. Monte Carlo studies reveal the good and stable performance of our particle filter-based estimator. When the volatility of volatility is high, or when regressors are absent but stochastic volatility exists, our approach can be better than the maximum likelihood estimator which neglects stochastic volatility and generalized method of moments (GMM estimators.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Stochastic Volatility and Option Pricing in Heath-Jarrow-Morton Term Structure Analysis
Skovmand, David
We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented.......We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented....
Bessac, Julie; Ailliot, Pierre; Cattiaux, Julien; Monbet, Valerie
2016-02-01
Several multi-site stochastic generators of zonal and meridional components of wind are proposed in this paper. A regime-switching framework is introduced to account for the alternation of intensity and variability that is observed in wind conditions due to the existence of different weather types. This modeling blocks time series into periods in which the series is described by a single model. The regime-switching is modeled by a discrete variable that can be introduced as a latent (or hidden) variable or as an observed variable. In the latter case a clustering algorithm is used before fitting the model to extract the regime. Conditional on the regimes, the observed wind conditions are assumed to evolve as a linear Gaussian vector autoregressive (VAR) model. Various questions are explored, such as the modeling of the regime in a multi-site context, the extraction of relevant clusterings from extra variables or from the local wind data, and the link between weather types extracted from wind data and large-scale weather regimes derived from a descriptor of the atmospheric circulation. We also discuss the relative advantages of hidden and observed regime-switching models. For artificial stochastic generation of wind sequences, we show that the proposed models reproduce the average space-time motions of wind conditions, and we highlight the advantage of regime-switching models in reproducing the alternation of intensity and variability in wind conditions.
Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThe paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace
Estimation in continuous-time stochastic| volatility models using nonlinear filters
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
A study about the existence of the leverage effect in stochastic volatility models
Florescu, Ionuţ; Pãsãricã, Cristian Gabriel
2009-02-01
The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage effect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility increases and vice versa. Consequently, it is important to demonstrate that any formulated model for the asset price is capable of generating this effect observed in practice. Furthermore, we need to understand the conditions on the parameters present in the model that guarantee the apparition of the leverage effect. In this paper we analyze two general specifications of stochastic volatility models and their capability of generating the perceived leverage effect. We derive conditions for the apparition of leverage effect in both of these stochastic volatility models. We exemplify using stochastic volatility models used in practice and we explicitly state the conditions for the existence of the leverage effect in these examples.
Adelie penguin foraging location predicted by tidal regime switching.
Matthew J Oliver
Full Text Available Penguin foraging and breeding success depend on broad-scale environmental and local-scale hydrographic features of their habitat. We investigated the effect of local tidal currents on a population of Adélie penguins on Humble Is., Antarctica. We used satellite-tagged penguins, an autonomous underwater vehicle, and historical tidal records to model of penguin foraging locations over ten seasons. The bearing of tidal currents did not oscillate daily, but rather between diurnal and semidiurnal tidal regimes. Adélie penguins foraging locations changed in response to tidal regime switching, and not to daily tidal patterns. The hydrography and foraging patterns of Adélie penguins during these switching tidal regimes suggest that they are responding to changing prey availability, as they are concentrated and dispersed in nearby Palmer Deep by variable tidal forcing on weekly timescales, providing a link between local currents and the ecology of this predator.
On cross-currency models with stochastic volatility and correlated interest rates
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of
On cross-currency models with stochastic volatility and correlated interest rates
Grzelak, L.A.; Oosterlee, C.W.
2010-01-01
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull
Approximation methods of European option pricing in multiscale stochastic volatility model
Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei
2017-01-01
In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.
Joint Pricing of VIX and SPX Options with Stochastic Volatility and Jump models
Kokholm, Thomas; Stisen, Martin
2015-01-01
and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures. The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed...
Christoffersen, Peter; Heston, Steven; Jacobs, Kris
State-of-the-art stochastic volatility models generate a "volatility smirk" that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However...... using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time...
Stochastic volatility models at ρ=±1 as second class constrained Hamiltonian systems
Contreras G., Mauricio
2014-07-01
The stochastic volatility models used in the financial world are characterized, in the continuous-time case, by a set of two coupled stochastic differential equations for the underlying asset price S and volatility σ. In addition, the correlations of the two Brownian movements that drive the stochastic dynamics are measured by the correlation parameter ρ (-1≤ρ≤1). This stochastic system is equivalent to the Fokker-Planck equation for the transition probability density of the random variables S and σ. Solutions for the transition probability density of the Heston stochastic volatility model (Heston, 1993) were explored in Dragulescu and Yakovenko (2002), where the fundamental quantities such as the transition density itself, depend on ρ in such a manner that these are divergent for the extreme limit ρ=±1. The same divergent behavior appears in Hagan et al. (2002), where the probability density of the SABR model was analyzed. In an option pricing context, the propagator of the bi-dimensional Black-Scholes equation was obtained in Lemmens et al. (2008) in terms of the path integrals, and in this case, the propagator diverges again for the extreme values ρ=±1. This paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum: all of them are second class constrained systems for the most extreme correlated limit ρ=±1. In this way, the stochastic dynamics of the ρ=±1 cases are different of the -1mechanics of the quantum model, implies that stochastic volatility models at ρ=±1 correspond to a constrained system. To study the dynamics in an appropriate form, Dirac's method for constrained systems (Dirac, 1958, 1967) must be employed, and Dirac's analysis reveals that the constraints are second class. In order to obtain the transition probability density or the option price correctly, one must evaluate the propagator as a constrained Hamiltonian path-integral (Henneaux and
AN EXAMINATION OF THE LEVERAGE EFFECT IN THE ISE WITH STOCHASTIC VOLATILITY MODEL
YELİZ YALÇIN
2013-06-01
Full Text Available The purpose of this paper is the asses the leverage effect of the Istanbul Stock Exchange within the Stochastic Volatility framework in the period 01.01.1990 – 11.08.2006. The relationship between risk and return is a well established phenomenon in Financial Econometerics. Both positive and negative relationship has been reported in the empirical literature. That use the conditional variance the empirical evidence provided in this paper from the Stochastic Volatility is to be negative feed back effect and statistically insignificant leverage effect.
Power and bipower variation with stochastic volatility and jumps (with discussion)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2004-01-01
This article shows that realized power variation and its extension, realized bipower variation, which we introduce here, are somewhat robust to rare jumps. We demonstrate that in special cases, realized bipower variation estimates integrated variance in stochastic volatility models, thus providing...... a model-free and consistent alternative to realized variance. Its robustness property means that if we have a stochastic volatility plus infrequent jumps process, then the difference between realized variance and realized bipower variation estimates the quadratic variation of the jump component...
The effects of crude oil shocks on stock market shifts behaviour A regime switching approach
Aloui, Chaker; Jammazi, Rania [International Finance Group-Tunisia, Faculty of Management and Economic Sciences of Tunis, Boulevard du 7 novembre, El Manar University, B.P. 248, C.P. 2092, Tunis Cedex (Tunisia)
2009-09-15
In this paper we develop a two regime Markov-switching EGARCH model introduced by Henry [Henry, O., 2009. Regime switching in the relationship between equity returns and short-term interest rates. Journal of Banking and Finance 33, 405-414.] to examine the relationship between crude oil shocks and stock markets. An application to stock markets of UK, France and Japan over the sample period January 1989 to December 2007 illustrates plausible results. We detect two episodes of series behaviour one relative to low mean/high variance regime and the other to high mean/low variance regime. Furthermore, there is evidence that common recessions coincide with the low mean/high variance regime. In addition, we allow both real stock returns and probability of transitions from one regime to another to depend on the net oil price increase variable. The findings show that rises in oil price has a significant role in determining both the volatility of stock returns and the probability of transition across regimes. (author)
Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process
Liuwei Zhou
2014-01-01
Full Text Available The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally.
Decoupling the short- and long-term behavior of stochastic volatility
Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko
behavior) from long memory and persistence (long-term behavior) in a simple and parsimonious way, which allows us to successfully model volatility at all intraday time scales. Our prime model is based on the so-called Brownian semistationary process and we derive a number of theoretical properties...... measures of close to two thousand individual US equities, we find that both roughness and persistence appear to be universal properties of volatility. Inspired by the empirical findings, we introduce a new class of continuous-time stochastic volatility models, capable of decoupling roughness (short-term...
The Risk-Return Tradeoff and Leverage Effect in a Stochastic Volatility-in-Mean Model
Christensen, Bent Jesper; Posedel, Petra
We study the risk premium and leverage effect in the S&P500 market using the stochastic volatility-in-mean model of Barndor¤-Nielsen & Shephard (2001). The Merton (1973, 1980) equilibrium asset pricing condition linking the conditional mean and conditional variance of discrete time returns...
Jiang, George J.; Sluis, Pieter J. van der
1999-01-01
While the stochastic volatility (SV) generalization has been shown to improve the explanatory power over the Black-Scholes model, empirical implications of SV models on option pricing have not yet been adequately tested. The purpose of this paper is to first estimate a multivariate SV model using th
Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models
Xuemei Gao
2014-01-01
Full Text Available The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999 for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.
On the source of stochastic volatility: Evidence from CAC40 index options during the subprime crisis
Slim, Skander
2016-12-01
This paper investigates the performance of time-changed Lévy processes with distinct sources of return volatility variation for modeling cross-sectional option prices on the CAC40 index during the subprime crisis. Specifically, we propose a multi-factor stochastic volatility model: one factor captures the diffusion component dynamics and two factors capture positive and negative jump variations. In-sample and out-of-sample tests show that our full-fledged model significantly outperforms nested lower-dimensional specifications. We find that all three sources of return volatility variation, with different persistence, are needed to properly account for market pricing dynamics across moneyness, maturity and volatility level. Besides, the model estimation reveals negative risk premium for both diffusive volatility and downward jump intensity whereas a positive risk premium is found to be attributed to upward jump intensity.
Free float and stochastic volatility: the experience of a small open economy
Selçuk, Faruk
2004-11-01
Following a dramatic collapse of a fixed exchange rate based inflation stabilization program, Turkey moved into a free floating exchange rate system in February 2001. In this paper, an asymmetric stochastic volatility model of the foreign exchange rate in Turkey is estimated for the floating period. It is shown that there is a positive relation between the exchange return and its volatility. Particularly, an increase in the return at time t results in an increase in volatility at time t+1. However, the effect is asymmetric: a decrease in the exchange rate return at time t causes a relatively less decrease in volatility at time t+1. The results imply that a central bank with a volatility smoothing policy would be biased in viewing the shocks to the exchange rate in favor of appreciation. The bias would increase if the bank is also following an inflation targeting policy.
Pricing foreign equity option under stochastic volatility tempered stable Lévy processes
Gong, Xiaoli; Zhuang, Xintian
2017-10-01
Considering that financial assets returns exhibit leptokurtosis, asymmetry properties as well as clustering and heteroskedasticity effect, this paper substitutes the logarithm normal jumps in Heston stochastic volatility model by the classical tempered stable (CTS) distribution and normal tempered stable (NTS) distribution to construct stochastic volatility tempered stable Lévy processes (TSSV) model. The TSSV model framework permits infinite activity jump behaviors of return dynamics and time varying volatility consistently observed in financial markets through subordinating tempered stable process to stochastic volatility process, capturing leptokurtosis, fat tailedness and asymmetry features of returns. By employing the analytical characteristic function and fast Fourier transform (FFT) technique, the formula for probability density function (PDF) of TSSV returns is derived, making the analytical formula for foreign equity option (FEO) pricing available. High frequency financial returns data are employed to verify the effectiveness of proposed models in reflecting the stylized facts of financial markets. Numerical analysis is performed to investigate the relationship between the corresponding parameters and the implied volatility of foreign equity option.
Canhanga, Betuel; Ni, Ying; Rančić, Milica; Malyarenko, Anatoliy; Silvestrov, Sergei
2017-01-01
After Black-Scholes proposed a model for pricing European Options in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption made by Black-Scholes was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced stochastic volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multifactor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented a semi-analytical formula to compute an approximate price for American options. The huge calculation involved in the Chiarella and Ziveyi approach motivated the authors of this paper in 2014 to investigate another methodology to compute European Option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present paper we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.
A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
Baaquie, Belal E.
1997-12-01
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.
A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility
Daniel Bonetti
2015-01-01
Full Text Available We propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to arbitrary square-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, the main merit of our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff. In particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. In order to demonstrate that our methodology is indeed applicable, we provide a Monte Carlo study on generalized Föllmer-Schweizer decompositions, locally risk minimizing, and mean variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.
Janssen, Anja; Mikosch, Thomas Valentin; Rezapour, Mohsen
2017-01-01
We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for the ordered eigenvalues and corresponding eigenvectors...... of the sample covariance matrix. While we show that in the case of heavy-tailed innovations the limiting behavior resembles that of completely independent observations, we also derive that in the case of a heavy-tailed volatility sequence the possible limiting behavior is more diverse, i.e. allowing...
ABC of SV: Limited Information Likelihood Inference in Stochastic Volatility Jump-Diffusion Models
Creel, Michael; Kristensen, Dennis
We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators and filters are computationally attractive relative...... to standard likelihood-based versions since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters...... stochastic volatility model for the dynamics of the S&P 500 equity index. We find evidence of the presence of a dynamic jump rate and in favor of a structural break in parameters at the time of the recent financial crisis. We find evidence that possible measurement error in log price is small and has little...
Regime Switches in the Risk-Return Trade-off
Ghysels, Eric; Guérin, Pierre; Marcellino, Massimiliano
2013-01-01
This paper deals with the estimation of the risk-return trade-off. We use a MIDAS model for the conditional variance and allow for possible switches in the risk-return relation through a Markov-switching specification. We find strong evidence for regime changes in the risk-return relation. This finding is robust to a large range of specifications. In the first regime characterized by low ex-post returns and high volatility, the risk-return relation is reversed, whereas the intuitive positive ...
First-passage and risk evaluation under stochastic volatility
Masoliver, Jaume; Perelló, Josep
2009-07-01
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and the hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain approximate forms of these probabilities which prove, among other interesting properties, the nonexistence of a mean-first-passage time. One significant result is the evidence of extreme deviations—which implies a high risk of default—when certain dimensionless parameter, related to the strength of the volatility fluctuations, increases. We confront the model with empirical daily data and we observe that it is able to capture a very broad domain of the hitting probability. We believe that this may provide an effective tool for risk control which can be readily applicable to real markets both for portfolio management and trading strategies.
Matthew Lorig; Ronnie Sircar
2015-01-01
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) when the risky...
On Investment-Consumption with Regime-Switching
Pirvu, Traian A
2011-01-01
In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representative investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switches according to a finite state Markov chain. The change in the discount rate leads to time inconsistencies of the investor's decisions. The randomness in our model is driven by a Brownian motion and Markov chain. Following Ekeland etc (2008) we introduce and characterize the equilibrium policies for power utility functions. Moreover, they are computed in closed form for logarithmic utility function. We show that a higher discount rate leads to a higher equilibrium consumption rate. Numerical experiments show the effect of both time preference and risk aversion on the equilibrium policies.
Does Energy Consumption Volatility Affect Real GDP Volatility? An Empirical Analysis for the UK
Abdul Rashid; Ozge Kandemir Kocaaslan
2013-01-01
This paper empirically examines the relation between energy consumption volatility and unpredictable variations in real gross domestic product (GDP) in the UK. Estimating the Markov switching ARCH model we find a significant regime switching in the behavior of both energy consumption and GDP volatility. The results from the Markov regime-switching model show that the variability of energy consumption has a significant role to play in determining the behavior of GDP volatilities. Moreover, the...
Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices
Haldrup, Niels; Nielsen, Morten Ø.
and regime switching reflecting congestion and non-congestion periods are empirically relevant and hence are features that need to be taken into account when modeling price behavior. In the present paper we further elaborate on the co-existence of long memory and regime switches by focusing on the effect......-congestion and congestion periods with excess demand in the one or the other region. Using data from the Nordic power exchange, Nord Pool, we find that the price dynamicsand long memory features of the price series generally are rather differentacross the different states. Also, there is evidence of fractional...
Option pricing for stochastic volatility model with infinite activity Lévy jumps
Gong, Xiaoli; Zhuang, Xintian
2016-08-01
The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.
A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models
Raúl Merino
2015-01-01
Full Text Available We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model, extending a previous decomposition formula for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used for this purpose are nonanticipative. In particular, we also see that equivalent results can be obtained by using Functional Itô Calculus. Using the same generalizing ideas, we also extend to nonexponential models the alternative call option price decomposition formula written in terms of the Malliavin derivative of the volatility process. Finally, we give a general expression for the derivative of the implied volatility under both the anticipative and the nonanticipative cases.
A Regime Switching Model of Schooling Choice as a Job Search Process
Yong Hyun Shin
2015-01-01
Full Text Available We propose a regime switching model of schooling choice as a job search process. We adopt a two-state Markov process and the derived coupled Bellman equations are solved by seeking the root of an auxiliary algebraic equation. Some numerical examples are also considered.
Andronikos Paliathanasis
2016-05-01
Full Text Available We perform a classification of the Lie point symmetries for the Black-Scholes-Merton Model for European options with stochastic volatility, σ, in which the last is defined by a stochastic differential equation with an Orstein-Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2 evolution partial differential equation in which the price of the option depends upon two independent variables, the value of the underlying asset, S, and a new variable, y. We find that for arbitrary functional form of the volatility, σ ( y , the (1 + 2 evolution equation always admits two Lie point symmetries in addition to the automatic linear symmetry and the infinite number of solution symmetries. However, when σ ( y = σ 0 and as the price of the option depends upon the second Brownian motion in which the volatility is defined, the (1 + 2 evolution is not reduced to the Black-Scholes-Merton Equation, the model admits five Lie point symmetries in addition to the linear symmetry and the infinite number of solution symmetries. We apply the zeroth-order invariants of the Lie symmetries and we reduce the (1 + 2 evolution equation to a linear second-order ordinary differential equation. Finally, we study two models of special interest, the Heston model and the Stein-Stein model.
Shelly Singhal
2016-10-01
Full Text Available Time series models investigating the linkages between various asset markets (Commodity and Equity in India have assumed a symmetric and linear relationship between them. They examine these interrelationships by assuming the presence of a uniform economic state. However the returns from commodity futures and stock market do not show a continuous trend but exhibit time varying behaviour i.e. the returns of stocks might be higher in a certain economic condition and it may fall as the economic environment changes due to financial crises, oil price rise, rupee depreciation etc. Similarly the return of commodities is also subject to variation with the changing economic conditions due to which the basic assumptions of stationary and linearity of time series models gets refuted. Therefore, this paper empirically examines the interrelationships between commodity futures (Energy, Metal and Agriculture and stock markets in dynamic economic states by employing Markov Regime Switching model proposed by Hamilton (2005 which has the capability of capturing temporal asymmetries and nonlinear dynamics of time series. For each market a composite index indicating the overall movement and performance of a particular investment asset has been considered. In order to provide robust results this paper uses daily data from 2006 to 2014 which significantly represents different states in the Indian Economy. The result of the study confirms the impact of economic environment on Indian commodity and stock markets and validates the presence of two distinct regimes: a “tranquil regime” representing the state of economic expansion and a “crisis regime” representing the state of economic decline. Additionally, the result confirms that commodities and stock markets oscillate between high and low volatility regimes and this movement is different across different commodity class (Energy, Metal and Agriculture. In a portfolio, when commodity futures are combined with stock
Hozman, J.; Tichý, T.
2016-12-01
The paper is based on the results from our recent research on multidimensional option pricing problems. We focus on European option valuation when the price movement of the underlying asset is driven by a stochastic volatility following a square root process proposed by Heston. The stochastic approach incorporates a new additional spatial variable into this model and makes it very robust, i.e. it provides a framework to price a variety of options that is closer to reality. The main topic is to present the numerical scheme arising from the concept of discontinuous Galerkin methods and applicable to the Heston option pricing model. The numerical results are presented on artificial benchmarks as well as on reference market data.
Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility
Xinfeng Ruan
2013-01-01
Full Text Available We study the equity premium and option pricing under jump-diffusion model with stochastic volatility based on the model in Zhang et al. 2012. We obtain the pricing kernel which acts like the physical and risk-neutral densities and the moments in the economy. Moreover, the exact expression of option valuation is derived by the Fourier transformation method. We also discuss the relationship of central moments between the physical measure and the risk-neutral measure. Our numerical results show that our model is more realistic than the previous model.
Pricing credit default swaps under a multi-scale stochastic volatility model
Chen, Wenting; He, Xinjiang
2017-02-01
In this paper, we consider the pricing of credit default swaps (CDSs) with the reference asset driven by a geometric Brownian motion with a multi-scale stochastic volatility (SV), which is a two-factor volatility process with one factor controlling the fast time scale and the other representing the slow time scale. A key feature of the current methodology is to establish an equivalence relationship between the CDS and the down-and-out binary option through the discussion of "no default" probability, while balancing the two SV processes with the perturbation method. An approximate but closed-form pricing formula for the CDS contract is finally obtained, whose accuracy is in the order of O(ɛ + δ +√{ ɛδ }) .
Stochastic model of financial markets reproducing scaling and memory in volatility return intervals
Gontis, V.; Havlin, S.; Kononovicius, A.; Podobnik, B.; Stanley, H. E.
2016-11-01
We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.
Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices
Haldrup, Niels; Nielsen, Morten Ø.
and regime switching reflecting congestion and non-congestion periods are empirically relevant and hence are features that need to be taken into account when modeling price behavior. In the present paper we further elaborate on the co-existence of long memory and regime switches by focusing on the effect......The functioning of electricity markets has experienced increasing complexityas a result of deregulation in recent years. Consequently this affects the multilateral price behaviour across regions with physical exchange of power. It has been documented elsewhere that features such aslong memory......-congestion and congestion periods with excess demand in the one or the other region. Using data from the Nordic power exchange, Nord Pool, we find that the price dynamicsand long memory features of the price series generally are rather differentacross the different states. Also, there is evidence of fractional...
On Optimal Proportional Reinsurance and Investment in a Markovian Regime-Switching Economy
Xin ZHANG; Tak Kuen SIU
2012-01-01
In this paper,the surplus of an insurance company is modeled by a Markovian regimeswitching diffusion process.The insurer decides the proportional reinsurance and investment so as to increase revenue.The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.
Walid Chkili; Duc Khuong Nguyen
2014-01-01
We use a regime-switching model approach to investigate the dynamic linkages between the exchange rates and stock market returns for the BRICS countries (Brazil, Russia, India, China and South Africa). The univariate analysis indicates that stock returns
van der Ploeg, A.P.C.; Boswijk, H.P.; de Jong, F.
2003-01-01
We propose a class of stochastic volatility (SV) option pricing models that is more flexible than the more conventional models in different ways. We assume the conditional variance of the stock returns to be driven by an affine function of an arbitrary number of latent factors, which follow mean-rev
Jinquan Liu; Chunyang Pang
2011-01-01
Since the latter half of 2010, a new round of inflation has gradually been manifesting in China. The debate regarding whether excess money supply is responsible for this inflation has attracted scholars to investigate the effects of money growth on inflation. In this paper, we use correlation analysis to confirm the comovement between growth of monetary aggregates and inflation. We explore the asymmetric effects of monetary policy on inflation using the Markov regime-switching model The empirical results show that monetary policy can be more effective in curbing inflation in a high inflation state than in boosting the price level in a low inflation state. However, simply tightening the money supply might not be sufficient to suppress the price level To this end, the Chinese Government should adopt other policies, such as supply stabilization policies, to help suppress the price level Our study can help policy-makers to determine the actual economic state and provides some policy implications for the current inflation.
Elisa Alòs
2008-01-01
Full Text Available We obtain a Hull and White type formula for a general jump-diffusion stochastic volatility model, where the involved stochastic volatility process is correlated not only with the Brownian motion driving the asset price but also with the asset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of the at-the-money implied volatility skew.
DOES ENERGY CONSUMPTION VOLATILITY AFFECT REAL GDP VOLATILITY? AN EMPIRICAL ANALYSIS FOR THE UK
Abdul Rashid
2013-10-01
Full Text Available This paper empirically examines the relation between energy consumption volatility and unpredictable variations in real gross domestic product (GDP in the UK. Estimating the Markov switching ARCH model we find a significant regime switching in the behavior of both energy consumption and GDP volatility. The results from the Markov regime-switching model show that the variability of energy consumption has a significant role to play in determining the behavior of GDP volatilities. Moreover, the results suggest that the impacts of unpredictable variations in energy consumption on GDP volatility are asymmetric, depending on the intensity of volatility. In particular, we find that while there is no significant contemporaneous relationship between energy consumption volatility and GDP volatility in the first (low-volatility regime, GDP volatility is significantly positively related to the volatility of energy utilization in the second (high-volatility regime.
Shuang Li
2014-01-01
Full Text Available We study the pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.
Friedrich Hubalek; Petra Posedel
2008-01-01
We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit estimator based on martingale estimating functions in a bivariate model that is not a diffusion, but admits jumps. It is assumed that both the quantities are observed on a discrete grid of fixed width, a...
Adélie penguin foraging location predicted by tidal regime switching.
Oliver, Matthew J; Irwin, Andrew; Moline, Mark A; Fraser, William; Patterson, Donna; Schofield, Oscar; Kohut, Josh
2013-01-01
Penguin foraging and breeding success depend on broad-scale environmental and local-scale hydrographic features of their habitat. We investigated the effect of local tidal currents on a population of Adélie penguins on Humble Is., Antarctica. We used satellite-tagged penguins, an autonomous underwater vehicle, and historical tidal records to model of penguin foraging locations over ten seasons. The bearing of tidal currents did not oscillate daily, but rather between diurnal and semidiurnal tidal regimes. Adélie penguins foraging locations changed in response to tidal regime switching, and not to daily tidal patterns. The hydrography and foraging patterns of Adélie penguins during these switching tidal regimes suggest that they are responding to changing prey availability, as they are concentrated and dispersed in nearby Palmer Deep by variable tidal forcing on weekly timescales, providing a link between local currents and the ecology of this predator.
The january effect across volatility regimes
Agnani, Betty; Aray, Henry
2007-01-01
Using a Markov regime switching model, this article presents evidence on the well-known January effect on stock returns. The specification allows a distinction to be drawn between two regimes, one with high volatility and other with low volatility. We obtain a time-varying January effect that is, in general, positive and significant in both volatility regimes. However, this effect is larger in the high volatility regime. In sharp contrast with most previous literature we find two major result...
Inflation Volatility and Growth in a Stochastic Small Open Economy: A Mixed Jump-Diffusion Approach
Isela Elizabeth Téllez-León
2011-12-01
Full Text Available The aim of this paper is to examine how inflation volatility affects economic growth in a small open economy. To reach this goal, a stochastic macroeconomic model with a financial sector and incomplete financial markets (due to the inclusion of jumps is developed. It is assumed that the general price level is driven by mixed diffusion-jump process, that is, a Brownian motion governs inflation and a Poisson process guides unexpected and sudden jumps in the price index. The economic growth rate is endogenously determined, in the equilibrium, as a function of parameters of the inflation process.El objetivo de esta investigación es examinar cómo la volatilidad en la inflación afecta el crecimiento económico en una economía pequeña y abierta. Para alcanzar este objetivo, se desarrolla un modelo macroeconómico estocástico con un sector financiero y con mercados financieros incompletos (debido a la inclusión de saltos. Se supone que el nivel general de precios es conducido por un proceso estocástico que combina difusiones con saltos, es decir, la inflación es gobernada por un movimiento browniano y los saltos bruscos e inesperados en el índice de precios se rigen por un proceso de Poisson. La tasa de crecimiento económico se determina endógenamente, en el equilibrio, en función de los parámetros del proceso que conduce a la inflación.
An empirical comparison of alternate regime-switching models for electricity spot prices
Janczura, Joanna [Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, 50-370 Wroclaw (Poland); Weron, Rafal [Institute of Organization and Management, Wroclaw University of Technology, 50-370 Wroclaw (Poland)
2010-09-15
One of the most profound features of electricity spot prices are the price spikes. Markov regime-switching (MRS) models seem to be a natural candidate for modeling this spiky behavior. However, in the studies published so far, the goodness-of-fit of the proposed models has not been a major focus. While most of the models were elegant, their fit to empirical data has either been not examined thoroughly or the signs of a bad fit ignored. With this paper we want to fill the gap. We calibrate and test a range of MRS models in an attempt to find parsimonious specifications that not only address the main characteristics of electricity prices but are statistically sound as well. We find that the best structure is that of an independent spike 3-regime model with time-varying transition probabilities, heteroscedastic diffusion-type base regime dynamics and shifted spike regime distributions. Not only does it allow for a seasonal spike intensity throughout the year and consecutive spikes or price drops, which is consistent with market observations, but also exhibits the 'inverse leverage effect' reported in the literature for spot electricity prices. (author)
Dias, Gustavo Fruet; Scherrer, Cristina; Papailias, Fotis
The price discovery literature investigates how homogenous securities traded on different markets incorporate information into prices. We take this literature one step further and investigate how these markets contribute to stochastic volatility (volatility discovery). We formally show...... that the realized measures from homogenous securities share a fractional stochastic trend, which is a combination of the price and volatility discovery measures. Furthermore, we show that volatility discovery is associated with the way that market participants process information arrival (market sensitivity...
Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model
Perello, J
2006-01-01
The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. This paper wants to go further on with the expOU model we have studied in Ref. 1 by exploring an aspect of practical interest. Having as a benchmark the parameters estimated from the Dow Jones daily data, we want to compute the price for the European option. This is actually done by Monte Carlo, running a large number of simulations. Our main interest is to "see" the effects of a long-range market memory from our expOU model in its subsequent European call option. We pay attention to the effects of the existence of a broad range of time scales in the volatility. We find that a richer set of time scales brings to a higher price of the option. This appears in clear contrast to the presence of memory ...
Market memory and fat tail consequences in option pricing on the expOU stochastic volatility model
Perelló, Josep
2007-08-01
The expOU stochastic volatility model is capable of reproducing fairly well most important statistical properties of financial markets daily data. Among them, the presence of multiple time scales in the volatility autocorrelation is perhaps the most relevant which makes appear fat tails in the return distributions. This paper wants to go further on with the expOU model we have studied in Ref. [J. Masoliver, J. Perelló, Quant. Finance 6 (2006) 423] by exploring an aspect of practical interest. Having as a benchmark the parameters estimated from the Dow Jones daily data, we want to compute the price for the European option. This is actually done by Monte Carlo, running a large number of simulations. Our main interest is to “see” the effects of a long-range market memory from our expOU model in its subsequent European call option. We pay attention to the effects of the existence of a broad range of time scales in the volatility. We find that a richer set of time scales brings the price of the option higher. This appears in clear contrast to the presence of memory in the price itself which makes the price of the option cheaper.
Maxim Ioan
2009-05-01
Full Text Available In our paper we build a reccurence from generalized Garman equation and discretization of 3-dimensional domain. From reccurence we build an algorithm for computing values of an option based on time, momentan volatility of support and value of support on a
E. Barndorff-Nielsen, Ole; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G* of Potthoff-Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
Barndorff-Nielsen, Ole E.; Benth, Fred Espen; Szozda, Benedykt
This paper generalizes the integration theory for volatility modulated Brownian-driven Volterra processes onto the space G∗ of Potthoff--Timpel distributions. Sufficient conditions for integrability of generalized processes are given, regularity results and properties of the integral are discussed...
Slah Bahloul
2017-03-01
Full Text Available The objective of this paper is to study the impact of conventional stock market return and volatility and various macroeconomic variables (including inflation rate, short-term interest rate, the slope of the yield curve and money supply on Islamic stock markets returns for twenty developed and emerging markets using Markov switching regression models. The empirical results for the period 2002–2014 show that both developed and emerging Islamic stock indices are influenced by conventional stock indices returns and money supply for both the low and high volatility regimes. However, the other macroeconomic variables fail to explain the dynamics of Islamic stock indices especially in the high volatility regime. Similar conclusions are obtained by using the MS-VAR model.
Imam Wahyudi
2014-08-01
Full Text Available Asia's inancial crisis in July 1997 affects currency, capital market, and real market throughout Asian countries. Countries in southeast region (ASEAN, including Indonesia, Malaysia, Philippines, Singapore, and Thailand, are some of the countries where the crisis hit the most. In these countries, where inancial sectors are far more developed than real sectors and the money market sectors, most of the economic activities are conducted in capital market. Movement in the capital market could be a proxy to describe the overall economic situation and therefore the prediction of it could be an early warning system of economic crises. This paper tries to investigate movement in ASEAN (Indonesia, Malaysia, Philippines, Singapore, and Thailand capital market to build an early warning system from inancial sectors perspective. This paper will be very beneicial for the government to anticipate the forthcoming crisis. The insight of this paper is from Hamilton (1990 model of regime switching process in which he divide the movement of currency into two regimes, describe the switching transition based on Markov process and creates different model for each regimes. Differ from Hamilton, our research focuses on index return instead of currency to model the regime switching. This research aimed to ind the probability of crisis in the future by combining the probability of switching and the probability distribution function of each regime. Probability of switching is estimated by categorizing the movement in index return into two regimes (negative return in regime 1 and positive return in regime 2 then measuring the proportion of switching to regime 1 in t given regime
Wang, Guochao; Wang, Jun
2017-01-01
We make an approach on investigating the fluctuation behaviors of financial volatility duration dynamics. A new concept of volatility two-component range intensity (VTRI) is developed, which constitutes the maximal variation range of volatility intensity and shortest passage time of duration, and can quantify the investment risk in financial markets. In an attempt to study and describe the nonlinear complex properties of VTRI, a random agent-based financial price model is developed by the finite-range interacting biased voter system. The autocorrelation behaviors and the power-law scaling behaviors of return time series and VTRI series are investigated. Then, the complexity of VTRI series of the real markets and the proposed model is analyzed by Fuzzy entropy (FuzzyEn) and Lempel-Ziv complexity. In this process, we apply the cross-Fuzzy entropy (C-FuzzyEn) to study the asynchrony of pairs of VTRI series. The empirical results reveal that the proposed model has the similar complex behaviors with the actual markets and indicate that the proposed stock VTRI series analysis and the financial model are meaningful and feasible to some extent.
Financial Crisis, Monetary Policy, and Stock Market Volatility in China
Cheng-si Zhang; Da-yin Zhang; Jeffery Breece
2011-01-01
This paper employs the Markov regime switching GARCH model to capture the nature of China's stock market volatility in 2003-2009. We find a significant regime shift in the volatility of the stock market when the People's Bank of China adopted an accommodative monetary policy in response to the global financial crisis of 2007-2008. After the structural change, China's stock market moved into a regime with increased volatility, which appears to be persisting into the near future. This finding s...
Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market
Huiling Wu
2016-01-01
Full Text Available This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.
Exploring the WTI crude oil price bubble process using the Markov regime switching model
Zhang, Yue-Jun; Wang, Jing
2015-03-01
The sharp volatility of West Texas Intermediate (WTI) crude oil price in the past decade triggers us to investigate the price bubbles and their evolving process. Empirical results indicate that the fundamental price of WTI crude oil appears relatively more stable than that of the market-trading price, which verifies the existence of oil price bubbles during the sample period. Besides, by allowing the WTI crude oil price bubble process to switch between two states (regimes) according to a first-order Markov chain, we are able to statistically discriminate upheaval from stable states in the crude oil price bubble process; and in most of time, the stable state dominates the WTI crude oil price bubbles while the upheaval state usually proves short-lived and accompanies unexpected market events.
Han, Shurong; Huang, Yeqing
2017-07-07
The study analysed the medical imaging technology business cycle from 1981 to 2009 and found that the volatility of consumption in Chinese medical imaging business was higher than that of the developed countries. The volatility of gross domestic product (GDP) and the correlation between consumption and GDP is also higher than that of the developed countries. Prior to the early 1990s the volatility of consumption is even higher than GDP. This fact makes it difficult to explain the volatile market using the standard one sector real economic cycle (REC) model. Contrary to the other domestic studies, this study considers a three-sector dynamical stochastic general equilibrium REC model. In this model there are two consumption sectors, whereby one is labour intensive and another is capital intensive. The more capital intensive investment sector only introduces technology shocks in the medical imaging market. Our response functions and Monte-Carlo simulation results show that the model can explain 90% of the volatility of consummation relative to GDP, and explain the correlation between consumption and GDP. The results demonstrated the significant correlation between the technological reform in medical imaging and volatility in the labour market on Chinese macro economy development.
Silva, A. Christian; Prange, Richard E.
2007-03-01
We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were able to identify mean reversion effect in our portfolio. Finally, we briefly discuss the potential practical effect of the virtual volatility on an investor asset allocation strategy.
A. Christian Silva; Prange, Richard E.
2006-01-01
We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were able to identify mean reversion effect in our portfolio. Finally, we briefly discuss the potential practical effect of the virtual volatility on an investor asset allocation st...
张素梅
2012-01-01
To describe the real volatility of stock returns, this paper provides a rational model through allowing for stochastic interest rate and stochastic volatility rate in the double exponential jump-diffusion model. Subsequently, a closed-form solution for European call option is derived under the proposed model. Furthermore, the effects of main parameters on option prices are analyzed using numerical simulation. Simulations show that the model is suitable for modeling real-market changes. Stock returns are negatively correlated with volatility and stochastic interest rate has a significant impact on long term option values.%为合理刻画股价实际变化趋势,在双指数跳扩散模型中通过允许利率随机和波动率随机建立了合理的市场模型;然后利用鞅方法推导了随机利率、随机波动率下双指数跳扩散模型的欧式期权定价的闭式解;最后通过数值模拟分析了模型的主要参数对期权定价的影响.数值结果显示:所提模型能够较好地刻画股价实际变化趋势,股票收益和波动率负相关,随机利率对短期到期期权影响几乎可以忽略,而对长期到期期权价格影响显著.
THE VALUATION OF AMERICAN PUT OPTIONS WITH STOCHASTIC VOLATILITY%随机波动率的美式期权定价
梅正阳; 李楚霖
2002-01-01
本文利用随机波动率状态有限Markov链,通过有限差分方法计算美式期权的价值.这种方法既避免了建立复杂的随机波动率模型,又较大程度地改进了常数波动率的计算结果,获得与真实结果比较接近数值解,推广了二项式概率树模型.%In this paper, by using finite difference method, set up the valuation of American put option model with stochastic volatility of finite Markov chains, obtained the values of American put option, that improved the results of constant volatility model and binomial probability tree model. The illustration shows that the value calculated by our model and algorithm approaches the real price closer more.
Pricing Volatility Referenced Assets
Alan De Genaro Dario
2006-12-01
Full Text Available Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993 stochastic volatility model. Additionally, the Heston (1993 model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.
Gallego, C.; Costa, A.; Cuerva, A.
2010-09-01
Since nowadays wind energy can't be neither scheduled nor large-scale storaged, wind power forecasting has been useful to minimize the impact of wind fluctuations. In particular, short-term forecasting (characterised by prediction horizons from minutes to a few days) is currently required by energy producers (in a daily electricity market context) and the TSO's (in order to keep the stability/balance of an electrical system). Within the short-term background, time-series based models (i.e., statistical models) have shown a better performance than NWP models for horizons up to few hours. These models try to learn and replicate the dynamic shown by the time series of a certain variable. When considering the power output of wind farms, ramp events are usually observed, being characterized by a large positive gradient in the time series (ramp-up) or negative (ramp-down) during relatively short time periods (few hours). Ramp events may be motivated by many different causes, involving generally several spatial scales, since the large scale (fronts, low pressure systems) up to the local scale (wind turbine shut-down due to high wind speed, yaw misalignment due to fast changes of wind direction). Hence, the output power may show unexpected dynamics during ramp events depending on the underlying processes; consequently, traditional statistical models considering only one dynamic for the hole power time series may be inappropriate. This work proposes a Regime Switching (RS) model based on Artificial Neural Nets (ANN). The RS-ANN model gathers as many ANN's as different dynamics considered (called regimes); a certain ANN is selected so as to predict the output power, depending on the current regime. The current regime is on-line updated based on a gradient criteria, regarding the past two values of the output power. 3 Regimes are established, concerning ramp events: ramp-up, ramp-down and no-ramp regime. In order to assess the skillness of the proposed RS-ANN model, a single
A Markov switching model of the conditional volatility of crude oil futures prices
Fong, Wai Mun; See, Kim Hock [Department of Finance and Accounting, National University of Singapore, 119260 Kent Ridge Cresent (Singapore)
2002-01-01
This paper examines the temporal behaviour of volatility of daily returns on crude oil futures using a generalised regime switching model that allows for abrupt changes in mean and variance, GARCH dynamics, basis-driven time-varying transition probabilities and conditional leptokurtosis. This flexible model enables us to capture many complex features of conditional volatility within a relatively parsimonious set-up. We show that regime shifts are clearly present in the data and dominate GARCH effects. Within the high volatility state, a negative basis is more likely to increase regime persistence than a positive basis, a finding which is consistent with previous empirical research on the theory of storage. The volatility regimes identified by our model correlate well with major events affecting supply and demand for oil. Out-of-sample tests indicate that the regime switching model performs noticeably better than non-switching models regardless of evaluation criteria. We conclude that regime switching models provide a useful framework for the financial historian interested in studying factors behind the evolution of volatility and to oil futures traders interested short-term volatility forecasts.
Optimal Portfolio Selection Including Option with Regime Switching%模式转换市场下含期权的投资组合问题
梁月; 王子亭; 王晓洁
2011-01-01
In this paper, we consider the optimal portfolio selection including option under a Markov modulated regime-switching market. We formulate the problem as an utility maximization problem over a finite time horizon and uncertain time horizon. By utilizing the dynamic programming principle, we derive a regime-switching HJB equation. We provide the optimal portfolio selection under different markets which depends on the corresponding parameters. In this paper, we also obtain an important result that the wealth invested in the risky assets and the wealth invested in the option have a linear relationship. And the linear relationships are different in different markets. Specially, we derive the expression of the value function when the utility function is power function.%在Markov调制的模式转换市场下研究含有期权的投资组合问题.采用最大化期望终时财富的效用为目标,考虑确定时间水平与不确定时间水平;应用动态规划原理与HJB模型进行求解,得到不同市场模式下的最优投资策略,并且投资策略依赖于不同模式下的参数;得出不同市场模式投资于股票与以股票为标的资产的期权的财富并不是唯一的,二者满足线性关系(系数依赖于模式转换参数);给出了幂函数型效用函数下的值函数的表达式.
It’s all about volatility of volatility
Grassi, Stefano; Santucci de Magistris, Paolo
2015-01-01
for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during...... the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters....
范堃
2013-01-01
This paper considers the valuation of guaranteed minimum death benefit in variable annuities under a regime-switching model. More specifically, the risk-free interest rate, the appreciation rate and the volatility of the reference investment fund are modulated by a continuous-time, finite-state, observable Markov chain. A regime-switching Esscher transform is adopted to select an equiva-lent martingale measure in the incomplete financial market. Inverse Fourier transform is used to derive an analytical pricing formula for the embedded option in variable annuity with guaranteed minimum death benefit. To calculate the fair guarantee charge, fast Fourier transform approach is applied. Numerical examples are provided to illustrate the practical implementation and the relationship between the fair guarantee charges and other parameters.%本文研究具备最低身故利益保证的变额年金的定价问题。该模型中，假设无风险利率，投资基金的波动率是被连续时间有限状态马尔科夫链所调制的。运用体制转换Esscher变换方法得到唯一的等价鞅测度。在风险中性测度下，通过逆傅里叶变换得到最低身故利益保证的变额年金中嵌入期权的定价公式，然后通过快速傅里叶变换进行求解，并对数值例子进行了分析比较。
Factorization Method for Asset Pricing in Regime Switching Problems%状态转换问题中资产定价的因子分解方法
周璟华; 何春雄
2011-01-01
当支付流既依赖于基础资产价格又受外界干预时,资产的定价问题通常用状态转换模型来刻画.以对数布朗运动为基础资产模型,通过对期望现值算子进行Wiener-Hopf分解,给出了计算永久支付流的期望现值的具体步骤,并针对具跌停和涨停两种具体情形,得到了资产价格的闭形式表达式.%If a payoff stream depends on both a fundamental and possible interventions of an authority, the asset pricing problem is usually characterized by regime switching models. The fundamental is modeled as geometric Brownian motion. By Wiener-Hopf factorization of an EPV (expected present value) operator, concrete steps are provided to calculate the EPV of a perpetual payoff stream. Furthermore, the closed-form expressions of asset prices with surged limit and decline limit are given.
Carlos Alexánder Grajales Correa
2007-07-01
Full Text Available En este trabajo se consideran los rendimientos diarios de un activo financiero con el propósito de modelar y comparar la densidad de probabilidad de la volatilidad estocástica de los retornos. Para tal fin, se proponen los modelos ARCH y sus extensiones, que son en tiempo discreto, así como un modelo empírico de volatilidad estocástica, desarrollado por Paul Wilmott. Para el caso discreto se muestran los modelos que permiten estimar la volatilidad condicional heterocedástica en un instante t del tiempo, t∈[1,T]. En el caso continuo se asocia un proceso de difusión de Itô a la volatilidad estocástica de la serie financiera, lo cual posibilita discretizar dicho proceso y simularlo para obtener densidades de probabilidad empíricas de la volatilidad. Finalmente se ilustran y se comparan los resultados obtenidos con las metodologías expuestas para el caso de las series financieras S&P 500 de EEUU, el Índice de Precios y Cotizaciones de la Bolsa Mexicana de Valores (IPC y el IGBC de Colombia.This work considers daily yields of financial assets in order to model and compare returns stochastic volatility probability density. For such aim, ARCH models and its extensions are proposed - they are in discrete time- as well as an Empirical Stochastic Volatility Model, developed by Paul Wilmott. For the discrete case, models that allow to estimate heteroscedasticity conditional volatility in a time, t, t,t∈[1,T], are shown. In the continuous case, there is an association of an Itô diffusion process to stochastic volatility of the financial series, which allows to write a discretization of this process and to simulate it to obtain empirical probabilistic densities from the volatility. Finally the results are illustrated and compared with methodologies exposed by the case of the financial series S&P 500 of the U.S.A., Index of Prices and Quotations of stock-market Mexican of Values (IPC and IGBC of Colombia.
Stochastic modelling of turbulence
Sørensen, Emil Hedevang Lohse
This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating...... is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has...
曹原
2015-01-01
本文研究了Heston随机波动率市场下，基于VaR约束下的动态最优投资组合问题。假设Heston随机波动率市场由一个无风险资产和一个风险资产构成，投资者的目标为最大化其终端的期望效用。与此同时，投资者将动态地评估其待选的投资组合的VaR风险，并将其控制在一个可接受的范围之内。本文在合理的假设下，使用动态规划的方法，来求解该问题的最优投资策略。在特定的参数范围内，利用数值方法计算出近似的最优投资策略和相应值函数，并对结果进行了分析。%This paper considers an optimal portfolio choice problem under Heston stochastic volatility model and a dynamic VaR constraint .Assume the financial market consists of one risky asset , like stock, whose price satis-fies a Heston stochastic volatility model and one risk-free asset, like bond.The investor aims to maximize the expected power utility of the terminal wealth .At the same time , the investor hopes to manage the portfolio risk by a dynamic VaR constraint , which means she will compute the VaR of her portfolio continually .Using the stochastic dynamic programming approach , we solve the problem numerically .Finally, economic implications are proposed to illustrate the impacts of Heston stochastic volatility and dynamic VaR constraint on the investor ’ s optimal strategy .Our numerical experiment shows that the dynamic VaR criterion is an effective tool to manage the risk during the whole investment period .
伊博; 李仲飞; 曾燕
2012-01-01
This paper considers an optimal portfolio choice problem under Stein-Stein stochastic volatility model and dynamic VaR constraint. The investor aims to maximize the expected power utility of the terminal wealth, and the financial market consists of one risk-free asset and one risky asset whose price process is described by Stein-Stein stochastic volatility model. At the same time, the investor hopes to limit the potential risk over investment horizon by a dynamic VaR constraint. Adopting the stochastic dynamic programming approach and Lagrange multiple method, we derive the closed-form expressions of the optimal strategy as well as the optimal value function in a special case. Moreover, economic implications and numerical analysis are proposed to illustrate the impacts of stochastic volatility and dynamic VaR constraint on the investor's optimal strategy.%研究Stein-Stein随机波动率模型下带动态VaR约束的最优投资组合选择问题.假设投资者的目标是最大化终端财富的期望幂效用,可投资于无风险资产和一种风险资产,风险资产的价格过程由Stein-Stein随机波动率模型刻画.同时,投资者期望能在投资过程中利用动态VaR约束控制所面对的风险.运用Bellman动态规划方法和Lagrange乘子法,得到了该约束问题最优策略的解析式及特殊情形下最优值函数的解析式；并通过理论分析和数值算例,阐述了动态VaR约束与随机波动率对最优投资策略的影响.
郝立亚; 朱慧明; 李素芳; 曾惠芳
2011-01-01
针对贝叶斯长记忆随机波动模型的单步Gibbs抽样算法效率低下的问题,通过对模型在状态空间框架下的近似表示,将向前滤波向后抽样算法引入对波动变量的估计过程中,同时在贝叶斯框架下分析了模型参数的满条件后验分布,设计出Gibbs联合抽样算法.更进一步,在对模型进行参数估计的基础上,提出波动变量的向前多步预报分布的估计方法.模拟实验结果表明:联合Gibbs抽样算法能够在保证估计精度的基础上得到优于单步Gibbs抽样方法的抽样效率,对预报分布的特征分析可用于对金融时间序列的风险控制.%This paper was concerned with simulation-based inference in generalized models of stochastic volatility with long memory. A more efficient Markov Chain Monte Carlo sampling method was exploited to the analysis of the model, compared with the single step Gibbs sampling method. Based on the truncated likelihood method, in which the long memory stochastic volatility model was expressed as a linear state space model, we utilized the forward filtering backward sampling method to sample all the unobserved volatilities simultaneously. A simulation method for Bayesian prediction analysis of the volatilities was also developed. The simulation study has given the results of estimated pa-rameters and evaluated the performance of our method. Moreover, the prediction analysis of the volatility can be used to control the risk of financial series.
樊顺厚; 马娟; 常浩
2016-01-01
应用随机最优控制方法研究 Heston随机波动率模型下带有负债过程的动态投资组合问题，其中假设股票价格服从 Heston随机波动率模型，负债过程由带漂移的布朗运动所驱动。金融市场由一种无风险资产和一种风险资产组成。应用随机动态规划原理和变量替换法得出了上述问题在幂效用和指数效用函数下最优投资策略的显示解，并给出数值算例分别分析了市场参数在幂效用和指数效用函数下对最优投资策略的影响。%The stochastic optimal control theory was used to study a dynamic portfolio selection problem with liability process under the Heston's stochastic volatility model.Stock price was assumed to be governed by the Hestonmodel,and the li-ability process was supposed to be driven by the drifted Brownian motion.The financial market consists of one risk-free asset and one risky asset.The explicit solutions to the optimal investment strategies under power utility and exponential utility were obtained by using stochastic dynamic programming principle and variable separation method.Finally,a numerical example was given to illustrate the effect of market parameters on the optimal investment strategy.
Hedging foreign exchange through regime-switching dynamic Copula model%基于状态转换动态Copula模型的外汇套期保值研究
唐韬; 谢赤
2015-01-01
汇改以来，人民币汇率波动的不确定性增大，外汇风险加剧，在此形势下加强外汇风险管理势在必行。考虑到利用外汇期货合约进行套期保值是管理外汇风险的一个重要方法，因此可建立一个状态转换动态 Gaussian Copula套期保值模型来对外汇风险进行管理。首先采用GJR-t模型描述欧元、日元、英镑、澳元和加元的现货和期货收益率的边际分布；然后引入状态转换动态 Copula 函数描述上述五种货币的现货和期货收益率之间的相关性；最后将状态转换动态Gaussian Copula模型与OLS，DCC GARCH，DCC Gaussian Copula等模型的套期保值效率进行比较。实证结果表明，所构建的模型优于其他模型，利用该策略模型能有效规避外汇风险。%Ever since the foreign currency exchange rate system reform in 2005, the indeterminacy of RMB exchange rate and the foreign exchange risk have greatly increased. Hence, it is immediately imperative to strengthen foreign exchange risk management. Considering that hedge by using foreign currency futures contracts is an important means of managing the foreign exchange risk, we can develop a hedging model based on regime-switching dynamic Copula model to manage the foreign exchange risk. Firstly, we can describe the spot and futures marginal distributions of EUR, JPY, GBP, AUD and CAD by using GJR-t model. Secondly, we can introduce regime-switching dynamic Copula model to tell the dependence between the spots and futures of EUR, JPY, GBP, AUD and CAD. Finally, a comparative analysis is conducted between regime-switching dynamic Copula model and OLS, DCC GARCH, DCC Gaussian Copula model. The empirical results show that the regime switching dynamic Copula model is superior to other models in the effect of hedging, and that hedging can mitigate the foreign exchange risk effectively.
张娇娇; 毕秀春; 李荣; 张曙光
2016-01-01
This study considers a stochastic volatility model for pricing perpetual American barrier options where the volatility is driven by a fast mean reversion Ornstein-Unlenbeck (O-U)process.It takes the case of the perpetual down-and-out call option for example,pricing problem of which can be formulated as a free boundary problem.Using the perturbation method,we first expand the price and the optimal exercise price of this option in the power of the length of mean reversion time.Then,by solving a set of Poisson equations,two asymptotic formulae are derived for this option price and the optimal exercise price,respectively.%研究波动率服从快速均值回复 Ornstein-Unlenbeck (O-U)过程的永久美式障碍期权的定价问题。考虑永久美式向下敲出看涨期权，该期权的定价问题可归结于求解自由边界问题。使用扰动法，把期权价格以及最优执行价格按均值回复时间长度的幂进行展开，通过求解 Poisson 方程组，得到期权和最优执行价格的渐近公式。
Optimal Portfolio Strategies with Mispricing and Stochastic Volatility%随机波动率市场存在股票误价时的最优投资策略
伊博; 李仲飞; 曾燕
2013-01-01
本文研究了随机波动率市场中存在股票误价(mispricing)时的最优投资组合选择问题.假设投资者的目标是最大化终端财富的期望幂效用;其可投资于无风险资产、市场指数和两支相同权益或近似度极高的股票,其中至少有一支股票存在误价；市场收益的波动率和股票系统风险由Heston随机波动率模型刻画.运用动态规划方法和Lagrange乘子法,分别得到不存在/存在有限卖空约束时,投资者的最优投资策略及最优值函数的解析式,并通过理论分析和数值算例,阐述了投资时间水平和价格随机误差对最优投资策略的影响.%This paper investigates an optimal portfolio selection problem in a market with mispricing and stochastic volatility.The investor's objective is to maximize the expected power utility of the terminal wealth,and the financial market consists of one risk-free asset,one risky asset representing the market index,and a pair of stocks whose prices are mispriced.Meanwhile,the volatilities of the market index and system risk are described by Heston stochastic volatility model.Without/with limited short selling constraints,the closed-form expressions of the optimal strategies and the optimal value functions are derived by the dynamic programming approach and the Lagrange multiple method.Moreover,economic implications and numerical examples are provided to illustrate that how the investment horizon and mispricing error affect the optimal strategies.
Yatracos, Yannis G.
2013-01-01
A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework. Strategies-probabilities $P_{t_0,n}$ and $P_{T,n}$ are thus determined and used, respectively,for the trader selling the share's European call option at time $t_0$ and for the buyer who may exercise it in the future, at $T; \\ n$ increases with the number of share's tr...
Some Recent Developments in Ambit Stochastics
Barndorff-Nielsen, Ole E.; Hedevang, Emil; Schmiegel, Jürgen
Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal la...... in turbulence and finance in relation to temporal processes (iii) Stochastic integration for time changed volatility modulated Levy-driven Volterra processes.......Some of the recent developments in the rapidly expanding field of Ambit Stochastics are here reviewed. After a brief recall of the framework of Ambit Stochastics three topics are considered: (i) Methods of modelling and inference for volatility/intermittency processes and fields (ii) Universal laws...
谢赤; 余聪; 罗长青; 王纲金
2013-01-01
构建了一个基于马尔可夫状态转换Copula函数的GJR-Skew-t模型,用以估计4个亚洲证券市场中股指期货与指数现货之间的最小方差套期保值比率.实证研究表明:动态套期保值模型的风险规避效果明显优于静态模型；根据套期保值组合方差降低百分比,该模型套期保值效果比其它动态策略有显著提升；除日本市场外,基于马尔可夫状态转换Copula函数的套期保值模型可以获得比传统模型更高的收益,这意味着该策略模型有助于降低套期保值成本.%This paper constructs a GJR-Skew-t model based on Copula functions with Markov regime switching to estimate the minimum variance hedging ratio between the returns of stock index futures and spots in four Asian markets. The empirical results show that the risk mitigation degree of the dynamic hedging models is higher than that of the static models. Based on the analysis of the variance reduction of hedging portfolio, the dynamic models are more effective than other models. Moreover, the proposed Markov regime-switching Copula-GJR-Skewed-t model can gain higher revenues than the traditional models except for the Japanese market, which means that our model contributes to reduce the cost of hedging.
王伟; 甘少波
2015-01-01
The problem of optimal investment and reinsurance policies based on a Markov regime switching model is studied. The dynamics of a risky asset is assumed to follow a Markov-modulated geometry Brownian motion, and an optimal investment and reinsurance policy by maximizes the expected exponential utility of terminal wealth is obtained. The results indicate that regime switching has a significant effect on the optimal investment strategies. In the end, the numerical analysis is provided which presents the effect of the market interest rate and absolute risk aversion parameter on the optimal investment and reinsurance policies.%研究了马尔可夫机制转换模型下保险公司的最优投资及再保险策略问题。假定风险资产价格满足马尔可夫调制的几何布朗运动，得到了最终财富的指数期望效用最大准则下的最优投资和最优再保险策略。结果表明：市场的经济状态对最优投资策略有很大影响，并通过数值计算分析了模型中市场利率和绝对风险厌恶系数与最优投资策略和最优再保险策略的关系。
J. Chen (Jinghui); M. Kobayashi (Masahito); M.J. McAleer (Michael)
2016-01-01
textabstractThe paper considers the problem as to whether financial returns have a common volatility process in the framework of stochastic volatility models that were suggested by Harvey et al. (1994). We propose a stochastic volatility version of the ARCH test proposed by Engle and Susmel (1993),
Stochastic Shadowing and Stochastic Stability
Todorov, Dmitry
2014-01-01
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
Daryl D. Rowan
2011-11-01
Full Text Available Volatile organic compounds (volatiles comprise a chemically diverse class of low molecular weight organic compounds having an appreciable vapor pressure under ambient conditions. Volatiles produced by plants attract pollinators and seed dispersers, and provide defense against pests and pathogens. For insects, volatiles may act as pheromones directing social behavior or as cues for finding hosts or prey. For humans, volatiles are important as flavorants and as possible disease biomarkers. The marine environment is also a major source of halogenated and sulfur-containing volatiles which participate in the global cycling of these elements. While volatile analysis commonly measures a rather restricted set of analytes, the diverse and extreme physical properties of volatiles provide unique analytical challenges. Volatiles constitute only a small proportion of the total number of metabolites produced by living organisms, however, because of their roles as signaling molecules (semiochemicals both within and between organisms, accurately measuring and determining the roles of these compounds is crucial to an integrated understanding of living systems. This review summarizes recent developments in volatile research from a metabolomics perspective with a focus on the role of recent technical innovation in developing new areas of volatile research and expanding the range of ecological interactions which may be mediated by volatile organic metabolites.
Optimal Portfolio Choice under Regime-switching and Learning Behaviors%状态变化和学习行为下的最优资产组合选择
陈志英
2013-01-01
针对金融资产收益率序列的非线性动态变化和投资者参数确定的传统假设,考虑状态变化的最优资产组合选择以及参数不确定性下投资者学习行为对最优资产组合选择的影响,运用马尔科夫机制转换模型刻画市场状态变化,采用贝叶斯学习准则描述投资者的学习行为,建立状态变化和投资者学习行为下资产组合选择的离散时间模型,使用期望最大化算法和动态最优化方法给出模型的参数估计,使用蒙特卡罗方法模拟投资者的资产组合选择行为.研究结果表明,中国金融市场存在明显的结构性动态变化,可以将市场分为牛市和熊市.在短期,当市场处于熊市时,投资者将全部财富投资于债券,不投资于股票,但市场处于牛市时股票的投资比重会大大增加；在长期,牛、熊市下股票和债券的权重会稳定在某个水平.市场状态的不确定性造成投资者产生对冲不确定性风险的需求,当市场向好时,投资者学习行为导致其投资于更多的风险资产；当市场状态无法确定时,投资者对股票的投资更为谨慎.考虑市场状态变化的投资组合选择能够提高投资者的总体效用.%Aiming at the nonlinear dynamic change of the financial asset return series and the traditional assumption of investor parameter certainty, the research explores the optimal portfolio choice under regime-switching and the impact of investors' learning behaviors under parameter uncertainty on the optimal portfolio choice. We use Markov regime-switching model to depict changes of market states, adopt the Bayesian learning rule to describe investors' learning behaviors, build the discrete model of optimal portfolio choice under regime-switching and learning behaviors, utilize the expectation maximization algorithm and dynamic optimization method to estimate the model parameters and make use of the Monte Carlo method to simulate investors' portfolio choice
Interest Rate Derivative Pricing with Stochastic Volatility
Chen, B.
2012-01-01
One purpose of exotic derivative pricing models is to enable financial institutions to quantify and manage their financial risk, arising from large books of portfolios. These portfolios consist of many non-standard exotic financial products. Risk is managed by means of the evaluation of sensitivity
Baldwin, Ian T
2010-05-11
Plant volatiles are the metabolites that plants release into the air. The quantities released are not trivial. Almost one-fifth of the atmospheric CO2 fixed by land plants is released back into the air each day as volatiles. Plants are champion synthetic chemists; they take advantage of their anabolic prowess to produce volatiles, which they use to protect themselves against biotic and abiotic stresses and to provide information - and potentially disinformation - to mutualists and competitors alike. As transferors of information, volatiles have provided plants with solutions to the challenges associated with being rooted in the ground and immobile.
Optimal dividend distribution under Markov regime switching
Jiang, Z.; Pistorius, M.
2012-01-01
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a determini
McKean, Henry P
2005-01-01
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen
Parzen, Emanuel
2015-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
马俊海; 张强
2012-01-01
本文首先基于诸多Libor市场模型改进方法的基础之上，在标准市场模型中加入Heston随机波动率过程，建立随机波动率假设的新型Libor市场模型；其次，运用Black逆推参数校正方法和MCMC参数估计方法对该Libor利率市场模型中的局部波动率和随机波动率过程中的参数进行校正和估计；最后是实证模拟。研究结论认为，在构建Libor利率动态模型时，若在单因子Libor利率市场模型基础上引入随机波动率过程，可大大提高利率模型的解释力。%In this paper, firstly, combining Heston stochastic volatility into standard market models, a new Libor market model is set up. Secondly, by using of Black inverse parameters calibrating methods and Markov Chain Monte Carlo simulation, we calibrate and estimate parameters of the new Libor market models. Lastly, we make an empirical analysis. The research conclusion is that Libor market model corporating into Heston stochastic volatility can improve greatly the explaination ability to interest rate models.
Schneider, Johannes J
2007-01-01
This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.
Casas, Isabel; Gijbels, Irène
2012-01-01
The objective of this paper is to introduce the break-preserving local linear (BPLL) estimator for the estimation of unstable volatility functions for independent and asymptotically independent processes. Breaks in the structure of the conditional mean and/or the volatility functions are common i...
Casas, Isabel; Gijbels, Irène
2012-01-01
The objective of this paper is to introduce the break-preserving local linear (BPLL) estimator for the estimation of unstable volatility functions for independent and asymptotically independent processes. Breaks in the structure of the conditional mean and/or the volatility functions are common i...
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Caporin, Massimiliano; Rossi, Eduardo; Santucci de Magistris, Paolo
The realized volatility of financial returns is characterized by persistence and occurrence of unpreditable large increments. To capture those features, we introduce the Multiplicative Error Model with jumps (MEM-J). When a jump component is included in the multiplicative specification, the condi...... models, the introduction of the jump component provides a sensible improvement in the fit, as well as for in-sample and out-of-sample volatility tail forecasts....
Zhiguang Wang
2009-01-01
Classical capital asset pricing theory tells us that riskaverse investors would require higher returns to compensate for higher risk on an investment. One type of risk is price (return) risk, which reflects uncertainty in the price level and is measured by the volatility (standard deviation) of asset returns. Volatility itself is also known to be random and hence is perceived as another type of risk. Investors can bear price risk in exchange for a higher return. But are investors willing to p...
Stochastic Constraint Programming
Walsh, Toby
2009-01-01
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number...
A novel Monte Carlo approach to hybrid local volatility models
A.W. van der Stoep (Anton); L.A. Grzelak (Lech Aleksander); C.W. Oosterlee (Cornelis)
2017-01-01
textabstractWe present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant.
Modelling of volatility in monetary transmission mechanism
Dobešová, Anna; Klepáč, Václav; Kolman, Pavel [Department of Statistics and Operation Analysis, Faculty of Business and Economics, Mendel University in Brno, Zemědělská 1, 61300, Brno (Czech Republic); Bednářová, Petra [Institute of Technology and Business, Okružní 517/10, 370 01, České Budějovice (Czech Republic)
2015-03-10
The aim of this paper is to compare different approaches to modeling of volatility in monetary transmission mechanism. For this purpose we built time-varying parameter VAR (TVP-VAR) model with stochastic volatility and VAR-DCC-GARCH model with conditional variance. The data from three European countries are included in the analysis: the Czech Republic, Germany and Slovakia. Results show that VAR-DCC-GARCH system captures higher volatility of observed variables but main trends and detected breaks are generally identical in both approaches.
Bisognano, J.; Leemann, C.
1982-03-01
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron.
A Stochastic Flows Approach for Asset Allocation with Hidden Economic Environment
Tak Kuen Siu
2015-01-01
Full Text Available An optimal asset allocation problem for a quite general class of utility functions is discussed in a simple two-state Markovian regime-switching model, where the appreciation rate of a risky share changes over time according to the state of a hidden economy. As usual, standard filtering theory is used to transform a financial model with hidden information into one with complete information, where a martingale approach is applied to discuss the optimal asset allocation problem. Using a martingale representation coupled with stochastic flows of diffeomorphisms for the filtering equation, the integrand in the martingale representation is identified which gives rise to an optimal portfolio strategy under some differentiability conditions.
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
吴吉林; 张二华
2012-01-01
通过构建机制转换混合Copula模型,考察了沪、深股市与港、台股市间的尾部相依特征,研究发现:它们间的尾部相依性呈非对称动态过程,在低风险状态下,右尾部相依性普遍高于左尾部相依性；而在高风险状态下,左尾部相依性普遍高于右尾部相依性.相对于沪、深股市与台股而言,沪、深股市与港股间的尾部相依性更强,其尾部相依性对外来冲击更敏感；相对于沪市与港、台股市而言,深市与港、台股市间的尾部对外在冲击更敏感.在此次次贷危机中,沪、深股市与港、台股市间极值风险显著增加,并呈现明显的金融感染.而且各尾部相依性的两个结构变化几乎同时发生并分别对应于危机的第一、二阶段,这表明:沪、深股市与港、台股市间的风险呈系统性特征,而危机的第三阶段对沪、深股市与港、台股市间的影响较有限.%Based on regime switching mixed Copula model, this paper finds the tail dependence between Shanghai, Shenzhen and Hongkong, Taiwan stock markets is a dynamic asymmetric process. In the state of low risk, right tail dependence is higher than left tail dependence; in the state of high risk, the situation is opposite. The tail dependence between Shanghai, Shenzhen and Hongkong stock markets is much stronger and more sensitive to exterior shocks than that between Shanghai, Shenzhen and Taiwan stock markets. The tail dependence between Shenzhen and Hongkong, Taiwan stock markets is more sensitive to exterior shocks than that between Shanghai and Hongkong, Taiwan stock markets. Tail dependence shows Chinese stock market risk increases significantly in the crisis and financial contagion happens. Furthermore, the tail dependence shows two big simultaneous structure changes correspond to the first and second stages of the crisis, which means the stock market risk is systematic. However, the third stage of the crisis almost has no influence on
OUTPUT VOLATILITY AND EXCHANGE RATE CONSIDERATIONS UNDER INFLATION TARGETING : A REVIEW
Marjan Petreski
2012-01-01
Full Text Available The objective of the paper is to offer a critique on the theoretical and empirical literature on inflation targeting (IT. It seems to exist a consensus in the theoretical literature that this monetary regime reduces both inflation and output volatility, mainly through building monetary policy credibility. When the role of the exchange rate is discussed, while there are some arguments that, as an instrument, it should not be explicitly stated in the central-bank loss function, theoretical arguments and evidence are still mixed as regards the effectiveness of exchange-rate management under IT. On the empirical front, the paper concludes that despite the fact that the work on IT in the last two decades has been immense in quality and quantity, still there is no quantitatively-credible study for the developing world, let alone a study that appropriately measures the regime switch from one monetary strategy to another.
Romanu Ekaterini
2006-01-01
Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.
Assessing relative volatility/intermittency/energy dissipation
Barndorff-Nielsen, Ole E.; Pakkanen, Mikko S.; Schmiegel, Jürgen
2014-01-01
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated by a non-semimartingale, or a Brownian semistationary...... process in particular. This estimation method is motivated by the assessment of relative energy dissipation in empirical data of turbulence, but it is also applicable in other areas. We develop a probabilistic asymptotic theory for realised relative power variations of Brownian semistationary processes......, and introduce inference methods based on the theory. We also discuss how to extend the asymptotic theory to other classes of processes exhibiting stochastic volatility/intermittency. As an empirical application, we study relative energy dissipation in data of atmospheric turbulence....
Neuro-Inspired Computing with Stochastic Electronics
Naous, Rawan
2016-01-06
The extensive scaling and integration within electronic systems have set the standards for what is addressed to as stochastic electronics. The individual components are increasingly diverting away from their reliable behavior and producing un-deterministic outputs. This stochastic operation highly mimics the biological medium within the brain. Hence, building on the inherent variability, particularly within novel non-volatile memory technologies, paves the way for unconventional neuromorphic designs. Neuro-inspired networks with brain-like structures of neurons and synapses allow for computations and levels of learning for diverse recognition tasks and applications.
A stochastic model of human gait dynamics
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Sobczyk, K
1985-01-01
This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.
Stochastic homothetically revealed preference for tight stochastic demand functions
Jan Heufer
2009-01-01
This paper strengthens the framework of stochastic revealed preferences introduced by Bandyopadhyay et al. (1999, 2004) for stochastic homothetically revealed preferences for tight stochastic demand functions.
Understanding the determinants of volatility clustering in terms of stationary Markovian processes
Miccichè, S.
2016-11-01
Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ-β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock's volatility is a linear function of the average correlation of such stock's volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts. As a result, the diagonalized volatilities result to share with the original volatilities either the power-law decay of the probability density function and the power-law decay of the autocorrelation function. This would indicate that volatility clustering is already present in the diagonalized un-correlated volatilities. We therefore present a parsimonious univariate model based on a non-linear Langevin equation that well reproduces these two stylized facts of volatility. The model helps us in understanding that the main source of volatility clustering, once volatilities have been diagonalized, is that the economic forces driving volatility can be modeled in terms of a Smoluchowski potential with logarithmic tails.
The stochastic integrable AKNS hierarchy
Arnaudon, Alexis
2015-01-01
We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose som...
Moawia Alghalith
2012-01-01
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Stochastic processes - quantum physics
Streit, L. (Bielefeld Univ. (Germany, F.R.))
1984-01-01
The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
Modeling the Implied Volatility Surface-: A Study for S&P 500 Index Option
Jin Zheng
2013-02-01
Full Text Available The aim of this study is to demonstrate a framework to model the implied volatilities of S&P 500 index options and estimate the implied volatilities of stock prices using stochastic processes. In this paper, three models are established to estimate whether the implied volatilities are constant during the whole life of options. We mainly concentrate on the Black-Scholes and Dumas’ option models and make the empirical comparisons. By observing the daily-recorded data of S&P 500 index, we study the volatility model and volatility surface. Results from numerical experiments show that the stochastic volatilities are determined by moneyness rather than constant. Our research is of vital importance, especially for forecasting stock market shocks and crises, as one of the applications.
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
A market model for stochastic smile: a conditional density approach
Zilber, A.
2005-01-01
The purpose of this paper is to introduce a new approach that allows to construct no-arbitrage market models of for implied volatility surfaces (in other words, stochastic smile models). That is to say, the idea presented here allows us to model prices of liquidly traded vanilla options as separate
Stochastic control with rough paths
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
马俊海; 张强
2013-01-01
LIBOR market model has played more and more important role in pricing financial assets and managing risk. FX structured deposits driven by LIBOR interest rate also have get more and more application. Therefore, it is very necessary to make theoretic estimation and Monte Carlo simulation for LIBOR interest rate process and its FX structured deposits pricing. In this paper, firstly, on the basic of many existing improved methods for LIBOR market models, combining Heston stochastic volatility into standard market models, we set up a new LIBOR market model. Secondly, by using of Black inverse parameters calibrating methods and Markov chain Monte Carlo simulation, we calibrate and estimate parameters of the new LIBOR market models. Thirdly, we use the improvement LSM to price this FX structured product. Lastly, we make an empirical analysis. The research conclusions are: 1) LIBOR market model with the stochastic volatility process can describe the LIBOR rate very well and display a finer accuracy. 2) The improvement LSM can get the much more precise result.%LIBOR市场利率已经在金融资产定价和风险度量中发挥着越来越重要的作用,而以其为标的利率的外汇结构性存款也得到了广泛应用.因此,对LIBOR利率动态过程及其结构性存款定价进行有效理论估计和模拟计算则显得尤为重要.本文首先在标准市场模型中加入Heston随机波动率过程,建立随机波动率过程驱动的新型LIBOR市场模型；其次,运用Black逆推参数校正方法和MCMC参数估计方法对该LIBOR利率市场模型中的局部波动率和随机波动率过程中的参数进行校正和估计；再次,基于最优基本函数改进的LSM方法对可赎回外汇结构性存款定价进行模拟计算；最后是实证分析.研究结论认为:在单因子LIBOR利率市场模型基础上引入随机波动率过程,则可大大地提高利率模型的解释力；基于最优基本函数改进的LSM定价方法所得结果
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
Volatility smile as relativistic effect
Kakushadze, Zura
2017-06-01
We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution (1) is properly normalized and (2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black-Scholes-Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no ;speed limit; and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Lévy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.
A conservative discontinuous target volatility strategy
Simone Cirelli
2017-07-01
Full Text Available The asset management sector is constantly looking for a reliable investment strategy, which is able to keep its promises. One of the most used approaches is the target volatility strategy that combines a risky asset with a risk-free trying to maintain the portfolio volatility constant over time. Several analyses highlight that such target is fulfilled on average, but in periods of crisis, the portfolio still suffers market’s turmoils. In this paper, the authors introduce an innovative target volatility strategy: the discontinuous target volatility. Such approach turns out to be more conservative in high volatility periods. Moreover, the authors compare the adoption of the VIX Index as a risk measure instead of the classical standard deviation and show whether the former is better than the latter. In the last section, the authors also extend the analysis to remove the risk-free assumption and to include the correlation structure between two risky assets. Empirical results on a wide time span show the capability of the new proposed strategy to enhance the portfolio performance in terms of standard measures and according to stochastic dominance theory.
A Simple Test for Causality in Volatility
Chia-Lin Chang
2017-03-01
Full Text Available An early development in testing for causality (technically, Granger non-causality in the conditional variance (or volatility associated with financial returns was the portmanteau statistic for non-causality in the variance of Cheng and Ng (1996. A subsequent development was the Lagrange Multiplier (LM test of non-causality in the conditional variance by Hafner and Herwartz (2006, who provided simulation results to show that their LM test was more powerful than the portmanteau statistic for sample sizes of 1000 and 4000 observations. While the LM test for causality proposed by Hafner and Herwartz (2006 is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and a test for which the (quasi- maximum likelihood estimates have valid asymptotic properties under the null hypothesis of non-causality. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger’s (1969, 1988 notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test.
Volatile Organic Compounds (VOCs)
... Contact Us Share Volatile Organic Compounds' Impact on Indoor Air Quality On this page: Introduction Sources Health Effects Levels in Homes Steps to Reduce Exposure Standards or Guidelines Additional Resources Introduction Volatile organic compounds ( ...
Fundamentals of Stochastic Networks
Ibe, Oliver C
2011-01-01
An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physi
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Stochastic longshore current dynamics
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
Du Xiaodong, E-mail: xdu23@wisc.ed [Department of Agricultural and Applied Economics, University of Wisconsin-Madison, WI (United States); Yu, Cindy L., E-mail: cindyyu@iastate.ed [Department of Statistics, Iowa State University, IA (United States); Hayes, Dermot J., E-mail: dhayes@iastate.ed [Department of Economics and Department of Finance, Iowa State University, IA (United States)
2011-05-15
This paper assesses factors that potentially influence the volatility of crude oil prices and the possible linkage between this volatility and agricultural commodity markets. Stochastic volatility models are applied to weekly crude oil, corn, and wheat futures prices from November 1998 to January 2009. Model parameters are estimated using Bayesian Markov Chain Monte Carlo methods. Speculation, scalping, and petroleum inventories are found to be important in explaining the volatility of crude oil prices. Several properties of crude oil price dynamics are established, including mean-reversion, an asymmetry between returns and volatility, volatility clustering, and infrequent compound jumps. We find evidence of volatility spillover among crude oil, corn, and wheat markets after the fall of 2006. This can be largely explained by tightened interdependence between crude oil and these commodity markets induced by ethanol production.
A Stochastic Employment Problem
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Stochastic Convection Parameterizations
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Verhoosel, C.V.; Gutiérrez, M.A.; Hulshoff, S.J.
2006-01-01
The field of fluid-structure interaction is combined with the field of stochastics to perform a stochastic flutter analysis. Various methods to directly incorporate the effects of uncertainties in the flutter analysis are investigated. The panel problem with a supersonic fluid flowing over it is con
Bollerslev, Tim; Gibson, Michael; Zhou, Hao
This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Car...... relate to a set of macro-finance state variables. We also find that the extracted volatility risk premium helps predict future stock market returns.......This paper proposes a method for constructing a volatility risk premium, or investor risk aversion, index. The method is intuitive and simple to implement, relying on the sample moments of the recently popularized model-free realized and option-implied volatility measures. A small-scale Monte Carlo...... experiment confirms that the procedure works well in practice. Implementing the procedure with actual S&P500 option-implied volatilities and high-frequency five-minute-based realized volatilities indicates significant temporal dependencies in the estimated stochastic volatility risk premium, which we in turn...
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Incomplete Continuous-time Securities Markets with Stochastic Income Volatility
Christensen, Peter Ove; Larsen, Kasper
2014-01-01
We derive closed-form solutions for the equilibrium interest rate and market price of risk processes in an incomplete continuous-time market with uncertainty generated by Brownian motions. The economy has a finite number of heterogeneous exponential utility investors, who receive partially...... equilibrium displays both lower interest rates and higher risk premia compared to the equilibrium in an otherwise identical complete market....
Stochastic decomposition and approximation of stock index return volatility
E. Capobianco (Enrico)
2001-01-01
textabstractWe show that decomposing a class of signals with overcomplete dictionaries of functions and combining multiresolution and independent component analysis allow for feature detection in complex non-stationary high frequency time series. Computational learning techniques are then designed
A Comparison of Biased Simulation Schemes for Stochastic Volatility Models
R. Lord (Roger); R. Koekkoek (Remmert); D.J.C. van Dijk (Dick)
2006-01-01
textabstractWhen using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at presen
Wenjie Bi
2014-01-01
Full Text Available Dynamic portfolio choice is an important problem in finance, but the optimal strategy analysis is difficult when considering multiple stochastic volatility variables such as the stock price, interest rate, and income. Besides, recent research in experimental economics indicates that the agent shows limited attention, considering only the variables with high fluctuations but ignoring those with small ones. By extending the sparse max method, we propose an approach to solve dynamic programming problem with small stochastic volatility and the agent’s bounded rationality. This approach considers the agent’s behavioral factors and avoids effectively the “Curse of Dimensionality” in a dynamic programming problem with more than a few state variables. We then apply it to Merton dynamic portfolio choice model with stochastic volatility and get a tractable solution. Finally, the numerical analysis shows that the bounded rational agent may pay no attention to the varying equity premium and interest rate with small variance.
Emerging Equity Market Volatility
Geert Bekaert; Harvey, Campbell R.
1995-01-01
Returns in emerging capital markets are very different from returns in developed markets. While most previous research has focused on average returns, we analyze the volatility of the returns in emerging equity markets. We characterize the time-series of volatility in emerging markets and explore the distributional foundations of the variance process. Of particular interest is evidence of asymmetries in volatility and the evolution of the variance process after periods of capital market refor...
Bollerslev, Tim; Sizova, Natalia; Tauchen, George
Stock market volatility clusters in time, carries a risk premium, is fractionally inte- grated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast......, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes....
陈晓红; 岳崴; 曹裕
2011-01-01
以2002-2009年深圳股市市场指数和22个行业指数为研究样本,本文运用不同的一阶马尔可夫过程刻画市场波动与行业系统性风险的状态转换行为,在此基础上估计了不同市场波动状态下行业系统性风险处于不同状态的条件概率,然后基于估计的条件概率探讨了行业系统性风险状态与市场波动状态之间的关联性.实证结果表明:市场波动和行业系统性风险均存在明显的两状态转换行为;其中采掘业等八个行业组合的系统性风险状态与市场波动状态之间存在正向的关联性;制造业等八个行业组合的系统性风险状态与市场波动状态之间存在反向的关联性;其他行业组合的系统性风险状态与市场波动状态之间不存在明显的关联性.可以利用行业系统性风险状态与市场波动状态之间的关联特性并根据市场波动状态的变化动态调整投资组合.
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Kraenkel, R. A.; da Silva, D. J. Pamplona
2010-01-01
We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.
Fundamentals of Stochastic Filtering
Crisan, Dan
2008-01-01
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
Wong, Yin Mei; Wilkie, Joshua
2006-01-01
Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary differential equations. Available methods for solving such equations have until recently been markedly inferior to analogous methods for deterministic ordinary differential equations. Recently, a number of methods which employ variable stepsizes to control local ...
Paweł Sakowski
2016-10-01
Full Text Available This article aims to extend evaluation of the classic multifactor model of Carhart (1997 for the case of global equity indices and to expand analysis performed in Sakowski et. al. (2015. Our intention is to test several modifications of these models to take into account different dynamics of equity excess returns between emerging and developed equity indices. Proposed extensions include a volatility regime switching mechanism (using dummy variables and the Markov approach and the fifth risk factor based on realized volatility of index returns. Moreover, instead of using data for stocks of a particular market (which is a common approach in the literature, we check performance of these models for weekly data of 81 world investable equity indices in the period of 2000-2015. Such an approach is proposed to estimate an equity risk premium for a single country. Empirical evidence reveals important differences between results for classical models estimated on single stocks (either in international or US-only frameworks and models evaluated for equity indices. Additionally, we observe substantial discrepancies between results for developed countries and emerging markets. Finally, using weekly data for the last 15 years we illustrate the importance of model risk and data overfitting effects when drawing conclusions upon results of multifactor models.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
Stochastic calculus with infinitesimals
Herzberg, Frederik
2013-01-01
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Distributive Disturbance and Optimai Policy in Stochastic Control Model
Wang Hongchu; Hu Shigeng; Zhang Xueqing
2006-01-01
To investigate the equilibrium relationships between the volatility of capital and income, taxation, and macroeconomic performance in a stochastic control model, the uniqueness of the solution to this model was proved by using the method of dynamic programming under the introduction of distributive disturbance and elastic labor supply. Furthermore, the effects of two types of shocks on labor-leisure choice, economic growth rate and welfare were numerically analyzed, and then the optimal tax policy was derived.
Notes on the Stochastic Exponential and Logarithm
Larsson, Martin; Ruf, Johannes
2017-01-01
Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.
Understanding Financial Market Volatility
A. Opschoor (Anne)
2014-01-01
markdownabstract__Abstract__ Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. Loosely speaking, volatility is defined as the average magnitude of fluctuations observed in some phenomenon over time. Wi
Improving Garch Volatility Forecasts
Klaassen, F.J.G.M.
1998-01-01
Many researchers use GARCH models to generate volatility forecasts. We show, however, that such forecasts are too variable. To correct for this, we extend the GARCH model by distinguishing two regimes with different volatility levels. GARCH effects are allowed within each regime, so that our model
Understanding Financial Market Volatility
A. Opschoor (Anne)
2014-01-01
markdownabstract__Abstract__ Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. Loosely speaking, volatility is defined as the average magnitude of fluctuations observed in some phenomenon over
Volatile metabolites from actinomycetes
Scholler, C.E.G.; Gurtler, H.; Pedersen, R.
2002-01-01
Twenty-six Streptomyces spp. were screened for their volatile production capacity on yeast starch agar. The volatile organic compounds (VOCs) were concentrated on a porous polymer throughout an 8-day growth period. VOCs were analyzed by gas chromatography with flame ionization detection and ident...
Geometric Stochastic Resonance
Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco
2015-01-01
A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.
Forecasting volatility of SSEC in Chinese stock market using multifractal analysis
Wei, Yu; Wang, Peng
2008-03-01
In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting performances of the MFV model and some other existing volatility models, such as the realized volatility model, stochastic volatility model and GARCH, are evaluated by the superior prediction ability (SPA) test. The empirical results show that under several loss functions, the MFV model obtains the best forecasting accuracy.
Idiosyncratic Volatility Puzzle
Aslanidis, Nektarios; Christiansen, Charlotte; Lambertides, Neophytos;
from a large pool of macroeconomic and Önancial variables. Cleaning for macro-Önance e§ects reverses the puzzling negative relation between returns and idiosyncratic volatility documented previously. Portfolio analysis shows that the e§ects from macro-Önance factors are economically strong......In this paper, we scrutinize the cross-sectional relation between idiosyncratic volatility and stock returns. As a novelty, the idiosyncratic volatility is obtained by conditioning upon macro-Önance factors as well as upon traditional asset pricing factors. The macro-Önance factors are constructed...
Pricing long-term options with stochastic volatility and stochastic interest rates
van Haastrecht, A.
2010-01-01
The markets for long-term options have expanded tremendously over the last decade. Nowadays many of these derivatives along with pension schemes and insurance products depend on joint changes in stock prices, interest rates and inflation. As a result the dependencies between the underlying assets ha
Quantum Spontaneous Stochasticity
Eyink, Gregory L
2015-01-01
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions for given initial data are unique. In fluid turbulence non-uniqueness due to "roughness" of the advecting velocity field is known to lead to stochastic motion of classical particles. Vanishingly small random perturbations are magnified by Richardson diffusion in a "nearly rough" velocity field so that motion remains stochastic as the noise disappears, or classical spontaneous stochasticity, . Analogies between stochastic particle motion in turbulence and quantum evolution suggest that there should be quantum spontaneous stochasticity (QSS). We show this for 1D models of a particle in a repulsive potential that is "nearly rough" with $V(x) \\sim C|x|^{1+\\alpha}$ at distances $|x|\\gg \\ell$ , for some UV cut-off $\\ell$, and for initial Gaussian wave-packet centered at 0. We consi...
Billings, M.B.; Jennings, R.; Lev, B.
2013-01-01
Survey evidence suggests that managers voluntarily disclose information, particularly earnings guidance, with an aim toward dampening share price volatility. Yet, consultants and influential institutions advise against providing guidance — citing fears of litigation and market penalties associated w
Dorn, Jochen
profit on well-developed markets. Dynamic participation features on cross asset portfolios are at rst sight a remedy to that dilemma. Based on volatility thresholds and portfolio re-balancing, the fund engineers try to create a "volatility guaranteed" investment opportunity by surfing on the unusual high...... concepts, next to nothing is known about position reverting strategies and how, and -even more important- in which context they are applied in practice. In the recent market downturn only one sector generated signicant profits for the leading investment banks: Volatility trading activities, namely on Forex......, interest rates and commodities. If an investor positions himself on the (volatility) market within a long/short trading framework, he typically bets on a traditional mispricing arbitrage. However as this corresponds to a call spread with equal exercise prices, this strategy alone would not generate enough...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Lacaze, Pierre-Camille
2014-01-01
Written for scientists, researchers, and engineers, Non-volatile Memories describes the recent research and implementations in relation to the design of a new generation of non-volatile electronic memories. The objective is to replace existing memories (DRAM, SRAM, EEPROM, Flash, etc.) with a universal memory model likely to reach better performances than the current types of memory: extremely high commutation speeds, high implantation densities and retention time of information of about ten years.
Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah Rozita [School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor (Malaysia)
2014-06-19
Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio.
Static vs stochastic optimization: A case study of FTSE Bursa Malaysia sectorial indices
Mamat, Nur Jumaadzan Zaleha; Jaaman, Saiful Hafizah; Ahmad, Rokiah@Rozita
2014-06-01
Traditional portfolio optimization methods in the likes of Markowitz' mean-variance model and semi-variance model utilize static expected return and volatility risk from historical data to generate an optimal portfolio. The optimal portfolio may not truly be optimal in reality due to the fact that maximum and minimum values from the data may largely influence the expected return and volatility risk values. This paper considers distributions of assets' return and volatility risk to determine a more realistic optimized portfolio. For illustration purposes, the sectorial indices data in FTSE Bursa Malaysia is employed. The results show that stochastic optimization provides more stable information ratio.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Stochastic Electrochemical Kinetics
Beruski, O
2016-01-01
A model enabling the extension of the Stochastic Simulation Algorithm to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a chemical master equation are provided and discussed. The electrochemical driving forces are included in the mathematical framework, and equations are provided for the associated electric responses. The implementation for potentiostatic and galvanostatic systems is presented, with results pointing out the stochastic nature of the algorithm. The electric responses presented are in line with the expected results from the theory, providing a new tool for the modeling of electrochemical kinetics.
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Markov stochasticity coordinates
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Stochastic integrals: a combinatorial approach
Rota, Gian-Carlo; Wallstrom, Timothy C.
1997-01-01
A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Stochastic integral equations without probability
Mikosch, T; Norvaisa, R
2000-01-01
A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0
stochastic process. Typical examples of such
Analysis of bilinear stochastic systems
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
The stochastic quality calculus
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...
Stochastic Control - External Models
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
D.F. Schrager
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing m
Wheeler, Tim Allan; Holder, Martin; Winner, Hermann; Kochenderfer, Mykel
2017-01-01
Accurate simulation and validation of advanced driver assistance systems requires accurate sensor models. Modeling automotive radar is complicated by effects such as multipath reflections, interference, reflective surfaces, discrete cells, and attenuation. Detailed radar simulations based on physical principles exist but are computationally intractable for realistic automotive scenes. This paper describes a methodology for the construction of stochastic automotive radar models based on deep l...
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
Limits for Stochastic Reaction Networks
Cappelletti, Daniele
at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...... of the stochastic reaction systems. Specically, we build a theory for stochastic reaction systems that is parallel to the deciency zero theory for deterministic systems, which dates back to the 70s. A deciency theory for stochastic reaction systems was missing, and few results connecting deciency and stochastic....... Such species, in the deterministic modelling regime, assume always the same value at any positive steady state. In the stochastic setting, we prove that, if the initial condition is a point in the basin of attraction of a positive steady state of the corresponding deterministic model and tends to innity...
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
Volatiles in protoplanetary disks
Pontoppidan, Klaus M; Bergin, Edwin A; Brittain, Sean; Marty, Bernard; Mousis, Olvier; Oberg, Karin L
2014-01-01
Volatiles are compounds with low sublimation temperatures, and they make up most of the condensible mass in typical planet-forming environments. They consist of relatively small, often hydrogenated, molecules based on the abundant elements carbon, nitrogen and oxygen. Volatiles are central to the process of planet formation, forming the backbone of a rich chemistry that sets the initial conditions for the formation of planetary atmospheres, and act as a solid mass reservoir catalyzing the formation of planets and planetesimals. This growth has been driven by rapid advances in observations and models of protoplanetary disks, and by a deepening understanding of the cosmochemistry of the solar system. Indeed, it is only in the past few years that representative samples of molecules have been discovered in great abundance throughout protoplanetary disks - enough to begin building a complete budget for the most abundant elements after hydrogen and helium. The spatial distributions of key volatiles are being mapped...
Pricing Volatility of Stock Returns with Volatile and Persistent Components
Zhu, Jie
2009-01-01
This paper introduces a two-component volatility model based on first moments of both components to describe the dynamics of speculative return volatility. The two components capture the volatile and the persistent part of volatility, respectively. The model is applied to 10 Asia-Pacific stock...... markets. Their in-mean effects on returns are tested. The empirical results show that the persistent component is much more important for the volatility dynamic process than is the volatile component. However, the volatile component is found to be a significant pricing factor of asset returns for most...... markets. A positive or risk-premium effect exists between the return and the volatile component, yet the persistent component is not significantly priced for the return dynamic process....
Pricing Volatility of Stock Returns with Volatile and Persistent Components
Zhu, Jie
In this paper a two-component volatility model based on the component's first moment is introduced to describe the dynamic of speculative return volatility. The two components capture the volatile and persistent part of volatility respectively. Then the model is applied to 10 Asia-Pacific stock m......, a positive or risk-premium effect exists between return and the volatile component, yet the persistent component is not significantly priced for return dynamic process.......In this paper a two-component volatility model based on the component's first moment is introduced to describe the dynamic of speculative return volatility. The two components capture the volatile and persistent part of volatility respectively. Then the model is applied to 10 Asia-Pacific stock...... markets. Their in-mean effects on return are also tested. The empirical results show that the persistent component accounts much more for volatility dynamic process than the volatile component. However the volatile component is found to be a significant pricing factor of asset returns for most markets...
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Samuelson, Paul A.
1971-01-01
Because a commodity like wheat can be carried forward from one period to the next, speculative arbitrage serves to link its prices at different points of time. Since, however, the size of the harvest depends on complicated probability processes impossible to forecast with certainty, the minimal model for understanding market behavior must involve stochastic processes. The present study, on the basis of the axiom that it is the expected rather than the known-for-certain prices which enter into all arbitrage relations and carryover decisions, determines the behavior of price as the solution to a stochastic-dynamic-programming problem. The resulting stationary time series possesses an ergodic state and normative properties like those often observed for real-world bourses. PMID:16591903
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Stochastic calculus and applications
Cohen, Samuel N
2015-01-01
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Stochastic gravitoelectromagnetic inflation
Aguilar, J E M; Bellini, Mauricio
2006-01-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this paper, we study a stochastic treatment for the gravitoelectromagnetic components $A_B=(A_{\\mu},\\phi)$, on cosmological scales. We focus our study on the seed magnetic fields on super Hubble scales, which could play an important role in large scale structure formation of the universe.
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Stochastic Thermodynamics of Learning
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Stochastic Games. I. Foundations,
1982-04-01
stimulate discussion and critical coment. Requests for single copies of a Paper will be filled by the Cowles Foundation within the limits of the supply...underpinning for the theory of stochastic games. Section 2 is a reworking of the Bevley- Kohlberg result integrated with Shapley’s; the "black magic" of... Kohlberg : The values of the r-discount game, and the stationary optimal strategies, have Puiseaux expansions. L.. 11" 6 3. More generally, consider an
Stochastic gravitoelectromagnetic inflation
Madriz Aguilar, José Edgar; Bellini, Mauricio
2006-11-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this Letter, we study a stochastic treatment for the gravitoelectromagnetic components A=(A,φ), on cosmological scales. We focus our study on the seed magnetic fields on super-Hubble scales, which could play an important role in large scale structure formation of the universe.
Stochastic power system operation
Power, Michael
2010-01-01
This paper outlines how to economically and reliably operate a power system with high levels of renewable generation which are stochastic in nature. It outlines the challenges for system operators, and suggests tools and methods for meeting this challenge, which is one of the most fundamental since large scale power networks were instituted. The Ireland power system, due to its nature and level of renewable generation, is considered as an example in this paper.
Stochastic Thermodynamics of Learning
Goldt, Sebastian
2016-01-01
Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\\eta\\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit.
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours
Lang, Annika
2007-01-01
This thesis discusses several aspects of the simulation of stochastic partial differential equations. First, two fast algorithms for the approximation of infinite dimensional Gaussian random fields with given covariance are introduced. Later Hilbert space-valued Wiener processes are constructed out of these random fields. A short introduction to infinite-dimensional stochastic analysis and stochastic differential equations is given. Furthermore different definitions of numerical stability for...
Dorn, Jochen
concepts, next to nothing is known about position reverting strategies and how, and -even more important- in which context they are applied in practice. In the recent market downturn only one sector generated signicant profits for the leading investment banks: Volatility trading activities, namely on Forex...
Stock markets liberalization affects volatility?
Ioan Alin NISTOR; Maria-Lenuţa CIUPAC-ULICI; GHERMAN Mircea-Cristian
2012-01-01
Regarding the impact of liberalization, the results show that, in general, market opening is accompanied by a significant increase in market volatility. In particular, volatility tends to decrease due to large capital inflows and domestic growth.The study analyzes the impact of stock market liberalization on volatility in six emerging stock markets by using GARCH methodology. Theory on the effects of financial liberalization on volatility has been ambiguous, and empirical work has yielded con...
The exploitation of volatile oil
MENG Teng; ZHANG Da; TENG Xiangjin; LINing; HAO Zaibin
2007-01-01
Rose is a kind of favorite ornamental plant. This article briefly introduced the cultivation and the use of rose around the world both in ancient time and nowadays. Today, volatile oil becomes the mainstream of the rose industry. People pay attention to the effect of volatile oil; meanwhile, they speed up their research on extracting volatile oil and the ingredients.
Plant volatiles and the environment
Loreto, F.; Dicke, M.; Schnitzler, J.P.; Turlings, T.C.J.
2014-01-01
Volatile organic compounds emitted by plants represent the largest part of biogenic volatile organic compounds (BVOCs) released into our atmosphere. Plant volatiles are formed through many biochemical pathways, constitutively and after stress induction. In recent years, our understanding of the func
Modeling neck linker of kinesin motor movement with MRSR stochastic differential equation
Razali, Wan Qashishah Akmal Wan; Ramli, Siti Norafidah Mohd; Radiman, Shahidan
2016-11-01
Stochastic differential equation has a significant role in a range of biological areas including molecular motor like kinesin motor. Mean-reverting square root (MRSR) stochastic differential equation is commonly used in economics and finance areas. In this study, we use the MRSR stochastic differential equation to model neck linker motion of kinesin motor by considering the possibilities of rightward direction and occasionally in the leftward direction of kinesin movements. This neck linker docking model of kinesin motor incorporates the conformational change in the chemical kinetics and the tethered diffusion of the free head of kinesin motor. Here, we demonstrate this model by using Hookean spring method which referred to the stiffness model of neck linker. The motion of kinesin motor seems to be well described to move in unidirectional way with volatile behavior based on MRSR rather than common stochastic differential equation [DOI 10.1007/s11538-011-9697-6].
Some stochastic aspects of quantization
Ichiro Ohba
2002-08-01
From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic ﬁeld equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.
Stochastic Analysis of Cylindrical Shell
Grzywiński Maksym
2014-06-01
Full Text Available The paper deals with some chosen aspects of stochastic structural analysis and its application in the engineering practice. The main aim of the study is to apply the generalized stochastic perturbation techniques based on classical Taylor expansion with a single random variable for solution of stochastic problems in structural mechanics. The study is illustrated by numerical results concerning an industrial thin shell structure modeled as a 3-D structure.
Verification of Stochastic Process Calculi
Skrypnyuk, Nataliya
Stochastic process calculi represent widely accepted formalisms within Computer Science for modelling nondeterministic stochastic systems in a compositional way. Similar to process calculi in general, they are suited for modelling systems in a hierarchical manner, by explicitly specifying...... subsystems as well as their interdependences and communication channels. Stochastic process calculi incorporate both the quantified uncertainty on probabilities or durations of events and nondeterministic choices between several possible continuations of the system behaviour. Modelling of a system is often...
Stochastic Nature in Cellular Processes
刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa
2011-01-01
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.
Mesoscopic Fluctuations in Stochastic Spacetime
Shiokawa, K
2000-01-01
Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.
A recurrent stochastic binary network
赵杰煜
2001-01-01
Stochastic neural networks are usually built by introducing random fluctuations into the network. A natural method is to use stochastic connections rather than stochastic activation functions. We propose a new model in which each neuron has very simple functionality but all the connections are stochastic. It is shown that the stationary distribution of the network uniquely exists and it is approximately a Boltzmann-Gibbs distribution. The relationship between the model and the Markov random field is discussed. New techniques to implement simulated annealing and Boltzmann learning are proposed. Simulation results on the graph bisection problem and image recognition show that the network is powerful enough to solve real world problems.
Stochastic Physicochemical Dynamics
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Scaling Foreign Exchange Volatility
Jonathan Batten; Craig Ellis
2001-01-01
When asset returns are normally distributed the risk of an asset over a long return interval may be estimated by scaling the risk from shorter return intervals. While it is well known that asset returns are not normally distributed a key empirical question concerns the effect that scaling the volatility of dependent processes will have on the pricing of related financial assets. This study provides an insight into this issue by investigating the return properties of the most important currenc...
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Deduction as Stochastic Simulation
2013-07-01
Eab Oa b Eab Ob a Iab Aab Iab Aba Iab Eab Iab EbaIab Iab Iab Iba Iab Oa b Iab Ob a Oa bAa b Oa bAb a Oa bEa b Oa bEb a Oa bIa b Oa bIb a Oa bO ab Oa bO...Oa bIa b Oa bIb a Oa bO ab Oa bO ba % C or re ct A. B. stochastic system’s parameters could be tweaked for individual reasoners. For example, the λ
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A
2016-01-01
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...
Mixed effects in stochastic differential equation models
Ditlevsen, Susanne; De Gaetano, Andrea
2005-01-01
maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...
Stochastic Pi-calculus Revisited
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic ferromagnetism analysis and numerics
Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas
2013-01-01
This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Stochastic Pi-calculus Revisited
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic power flow modeling
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
Recursive Concurrent Stochastic Games
Etessami, Kousha
2008-01-01
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [16,17] to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \\epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \\epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy r...
AA, stochastic precooling pickup
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...
Stochastic Blind Motion Deblurring
Xiao, Lei
2015-05-13
Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Variance decomposition in stochastic simulators
Le Maître, O. P.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Volatility Spillovers in Capesize Forward Freight Agreement Markets
Xiaoxing Gong
2016-01-01
Full Text Available This paper is to investigate spillovers in the Capesize forward freight agreements (FFAs markets before and after the global financial crisis. The paper chooses four Capesize voyage routes FFAs (C3, C4, C5, and C7, two time-charter routes FFAs (BCIT/C average, BPI T/C average, and spot rates as research subjects, covering the periods 3 January 2006 to 24 December 2015. This paper applies Volatility Spillover Multivariate Stochastic Volatility (VS-MSV model to analyze volatility spillover effects and estimates the parameters via software of Bayesian inference using Gibbs Sampling (BUGS, the deviance information criterion (DIC used for goodness-of-fit model. The results suggest that there are volatility spillover effects in certain Capesize FFAs routes, and the effects from spot rates to FFAs take place before crisis, yet they are bilateral after crisis. With the development of shipping markets, the correlations between FFAs and spot rate are enhanced, and it seems that the effects depend on market information and traders’ behavior. So practitioners could make decisions according to the spillovers.
Yang, Bo; Zhang, Xiao; Zhang, Lu; Luo, Mao-Kang
2016-08-01
The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.
Option Pricing using Realized Volatility
Stentoft, Lars Peter
In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate...... benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes....
Option Pricing using Realized Volatility
Stentoft, Lars Peter
In the present paper we suggest to model Realized Volatility, an estimate of daily volatility based on high frequency data, as an Inverse Gaussian distributed variable with time varying mean, and we examine the joint properties of Realized Volatility and asset returns. We derive the appropriate d...... benchmark model estimated on return data alone. Hence the paper provides evidence on the value of using high frequency data for option pricing purposes....
Stochastic Engine Convergence Diagnostics
Glaser, R
2001-12-11
The stochastic engine uses a Markov Chain Monte Carlo (MCMC) sampling device to allow an analyst to construct a reasonable estimate of the state of nature that is consistent with observed data and modeling assumptions. The key engine output is a sample from the posterior distribution, which is the conditional probability distribution of the state of nature, given the data. In applications the state of nature may refer to a complicated, multi-attributed feature like the lithology map of a volume of earth, or to a particular related parameter of interest, say the centroid of the largest contiguous sub-region of specified lithology type. The posterior distribution, which we will call f, can be thought of as the best stochastic description of the state of nature that incorporates all pertinent physical and theoretical models as well as observed data. Characterization of the posterior distribution is the primary goal in the Bayesian statistical paradigm. In applications of the stochastic engine, however, analytical calculation of the posterior distribution is precluded, and only a sample drawn from the distribution is feasible. The engine's MCMC technique, which employs the Metropolis-Hastings algorithm, provides a sample in the form of a sequence (chain) of possible states of nature, x{sup (1)}, x{sup (2)}, ..., x{sup (T)}, .... The sequencing is motivated by consideration of comparative likelihoods of the data. Asymptotic results ensure that the sample ultimately spans the entire posterior distribution and reveals the actual state frequencies that characterize the posterior. In mathematical jargon, the sample is an ergodic Markov chain with stationary distribution f. What this means is that once the chain has gone a sufficient number of steps, T{sub 0}, the (unconditional) distribution of the state, x{sup (T)}, at any step T {ge} T{sub 0} is the same (i.e., is ''stationary''), and is the posterior distribution, f. We call T{sub 0} the &apos
Stochastic population theories
Ludwig, Donald
1974-01-01
These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the Na...
Crystallization by stochastic flips
Bodini, Olivier; Fernique, Thomas; Regnault, Damien
2010-04-01
Tilings are often used as a toy model for quasicrystals, with the ground states corresponding to the tilings satisfying some local properties (matching rules). In this context, a challenging problem is to provide a theory for quasicrystals growth. One of the proposed theories is the relaxation process. One assumes that the entropy of a tiling increases with the number of tilings which can be formed with the same tiles, while its energy is proportional to the ratio of satisfied matching rules. Then, by starting from an entropically stabilized tiling at high temperature and by decreasing the temperature, the phason flips which decrease (resp. increase) the energy would become more and more favoured (resp. inhibited). Ideally, the tiling eventually satisfies all the matching rules, and thus shows a quasicrystalline structure. This paper describes a stochastic process inspired by this and discusses its convergence rate.
Stochastic reconstruction of sandstones
Manwart; Torquato; Hilfer
2000-07-01
A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and "pore size" distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples.
Stochastic dynamic equations on general time scales
Martin Bohner
2013-02-01
Full Text Available In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense.
Overview of Stochastic Vehicle Routing Problems
郭耀煌; 谢秉磊; 郭强
2002-01-01
Stochastic vehicle routing problems (VRPs) play important roles in logistics, though they have not been studied systematically yet. The paper summaries the definition, properties and classification of stochastic VRPs, makes further discussion about two strategies in stochastic VRPs, and at last overviews dynamic and stochastic VRPs.
An introduction to probability and stochastic processes
Melsa, James L
2013-01-01
Geared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
Frequency Resonance in Stochastic Systems
钱敏; 张雪娟
2003-01-01
The phenomenon of frequency resonance, which is usually related to deterministic systems, is investigated in stochastic systems. We show that for those autonomous systems driven only by white noise, if the output power spectrum exhibits a nonzero peak frequency, then applying a periodic signel just on this noise-induced central frequency can also induce a resonance phenomenon, which we call the frequency stochastic resonance. The effect of such a resonance in a coupled stochastic system is shown to be much better than that in a single-oscillator system.
Stochastic simulation in systems biology
Tamás Székely Jr.
2014-11-01
There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Introduction to stochastic dynamic programming
Ross, Sheldon M; Lukacs, E
1983-01-01
Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist-providing counterexamples where appropriate-and the
Volatile signals during pregnancy.
Vaglio, Stefano
2010-01-01
Scents play a key role in mediating reproductive interactions in many vertebrates including mammals. Nowadays, several studies indicate that humans seem to use remarkably olfactory communication and are even able to produce and perceive pheromones. Furthermore, over the past several years, it became increasingly clear that pheromone-like chemical signals probably play a role in offspring identification and mother recognition. Recently developed technical procedures (solid-phase microextraction and dynamic headspace extraction) now allow investigators to characterize volatile compounds with high reliability. We analyzed the volatile compounds in sweat patch samples collected from the para-axillary and nipple-areola regions of women during pregnancy and after childbirth. We hypothesized that, at the time of birth and during the first weeks of life, the distinctive olfactory pattern of the para-axillary area is probably useful to newborn babies for recognizing and distinguishing their own mother, whereas the characteristic pattern of the nipple-areola region is probably useful as a guide to nourishment.
Molecular plant volatile communication.
Holopainen, Jarmo K; Blande, James D
2012-01-01
Plants produce a wide array of volatile organic compounds (VOCs) which have multiple functions as internal plant hormones (e.g., ethylene, methyl jasmonate and methyl salicylate), in communication with conspecific and heterospecific plants and in communication with organisms of second (herbivores and pollinators) and third (enemies of herbivores) trophic levels. Species specific VOCs normally repel polyphagous herbivores and those specialised on other plant species, but may attract specialist herbivores and their natural enemies, which use VOCs as host location cues. Attraction of predators and parasitoids by VOCs is considered an evolved indirect defence, whereby plants are able to indirectly reduce biotic stress caused by damaging herbivores. In this chapter we review these interactions where VOCs are known to play a crucial role. We then discuss the importance of volatile communication in self and nonself detection. VOCs are suggested to appear in soil ecosystems where distinction of own roots from neighbours roots is essential to optimise root growth, but limited evidence of above-ground plant self-recognition is available.
Uniqueness of stochastic entropy solutions for stochastic balance laws with Lipschitz fluxes
Wei, Jinlong; Liu, Bin
2014-01-01
In this paper, we consider a stochastic balance law with a Lipschitz flux and gain the uniqueness for stochastic entropy solutions. The argument is supported by the stochastic kinetic formulation, the It\\^{o} formula and the regularization techniques. Furthermore, as an application, we derive the uniqueness of stochastic entropy solutions for stochastic porous media type equations.
Upper Bounds for Ruin Probabilities under Stochastic Interest Rate and Optimal Investment Strategies
Jin Zhu LI; Rong WU
2012-01-01
In this paper,we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond.We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross (CIR) model.For the stock price process,we consider both the case of constant volatility (driven by an O-U process) and the case of stochastic volatility (driven by a CIR model).In each case,under certain conditions,we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.
Stochastic analysis of laminated composite plate considering stochastic homogenization problem
S. SAKATA; K. OKUDA; K. IKEDA
2015-01-01
This paper discusses a multiscale stochastic analysis of a laminated composite plate consisting of unidirectional fiber reinforced composite laminae. In particular, influence of a microscopic random variation of the elastic properties of component materials on mechanical properties of the laminated plate is investigated. Laminated composites are widely used in civil engineering, and therefore multiscale stochastic analysis of laminated composites should be performed for reliability evaluation of a composite civil structure. This study deals with the stochastic response of a laminated composite plate against the microscopic random variation in addition to a random variation of fiber orientation in each lamina, and stochastic properties of the mechanical responses of the laminated plate is investigated. Halpin-Tsai formula and the homogenization theory-based finite element analysis are employed for estimation of effective elastic properties of lamina, and the classical laminate theory is employed for analysis of a laminated plate. The Monte-Carlo simulation and the first-order second moment method with sensitivity analysis are employed for the stochastic analysis. From the numerical results, importance of the multiscale stochastic analysis for reliability evaluation of a laminated composite structure and applicability of the sensitivity-based approach are discussed.
A Note on Almost Stochastic Dominance
Guo, Xu; Zhu, Xuehu; Wong, Wing-Keung; Zhu, Lixing
2013-01-01
To satisfy the property of expected-utility maximization, Tzeng et al. (2012) modify the almost second-degree stochastic dominance proposed by Leshno and Levy (2002) and define almost higher-degree stochastic dominance. In this note, we further investigate the relevant properties. We define an almost third-degree stochastic dominance in the same way that Leshno and Levy (2002) define second-degree stochastic dominance and show that Leshno and Levy's (2002) almost stochastic dominance has t...
Computer Auxiliary Analysis for Stochasticity of Chaos
ZHAOGeng; FANGJin-qing
2003-01-01
In this work, we propose a mathematics-physical statistic analytical method for stochastic process of chaos, based on stochastic test via combination measurement of Monobit and Runs. Computer auxiliary analysis shows that it is of stochasticity for stochastic number produced from the chaotic circuit. Our software is written by VB and C++, the later can be tested by the former, and at the same time it is verified by stochastic number produced by the computer. So the data treatment results are reliable.
Stochastic Climate Theory and Modelling
Franzke, Christian L E; Berner, Judith; Williams, Paul D; Lucarini, Valerio
2014-01-01
Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochast...
Stochastic Modelling of Hydrologic Systems
Jonsdottir, Harpa
2007-01-01
In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains an introduct......In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...
Detecting Stochastic Information of Electrocardiograms
Gutíerrez, R M; Guti'errez, Rafael M.; Sandoval, Luis A.
2003-01-01
In this work we present a method to detect, identify and characterize stochastic information contained in an electrocardiogram (ECG). We assume, as it is well known, that the ECG has information corresponding to many different processes related to the cardiac activity. We analyze scaling and Markov processes properties of the detected stochastic information using the power spectrum of the ECG and the Fokker-Planck equation respectively. The detected stochastic information is then characterized by three measures. First, the slope of the power spectrum in a particular range of frequencies as a scaling parameter. Second, an empirical estimation of the drift and diffusion coefficients of the Fokker-Planck equation through the Kramers-Moyal coefficients which define the evolution of the probability distribution of the detected stochastic information.
Stochastic Still Water Response Model
Friis-Hansen, Peter; Ditlevsen, Ove Dalager
2002-01-01
In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...... the stochastic cargo container load field is based on a queuing and loading policy that assumes containers are handled by a first-come-first-serve policy. The load field is assumed to be Gaussian. The ballast system is imposed to counteract the angle of heel and to regulate both the draft and the trim caused...
Stochastic Integration in Abstract Spaces
J. K. Brooks
2010-01-01
-valued process (∫ called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
Consistent ranking of volatility models
Hansen, Peter Reinhard; Lunde, Asger
2006-01-01
We show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility. For example, the substitution of a squared return for the conditional variance in the evaluation of ARCH-type models can...
Political institutions and economic volatility
Klomp, Jeroen; de Haan, Jakob
2009-01-01
We examine the effect of political 'institutions' on economic growth volatility, using data from more than 100 countries over the period 1960 to 2005, taking into account various control variables as suggested in previous studies. Our indicator of volatility is the relative standard deviation of the
Stochastic Analysis and Related Topics
Ustunel, Ali
1988-01-01
The Silvri Workshop was divided into a short summer school and a working conference, producing lectures and research papers on recent developments in stochastic analysis on Wiener space. The topics treated in the lectures relate to the Malliavin calculus, the Skorohod integral and nonlinear functionals of white noise. Most of the research papers are applications of these subjects. This volume addresses researchers and graduate students in stochastic processes and theoretical physics.
STochastic OPTimization library in C++
Gevret, Hugo; Lelong, Jerome; Warin, Xavier
2016-01-01
The STochastic OPTimization library (StOpt) aims at providing tools in C++ for solving somestochastic optimization problems encountered in finance or in the industry.A python binding is available for some C++ objects provided permitting to easily solve an optimization problem by regression.Different methods are available : dynamic programming methods based on Monte Carlo with regressions (global, local and sparse regressors), for underlying states following some uncontrolled Stochastic Differ...
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian, E-mail: grooms@cims.nyu.edu [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Majda, Andrew J., E-mail: jonjon@cims.nyu.edu [Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Center for Prototype Climate Modelling, NYU-Abu Dhabi (United Arab Emirates)
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Stochastic roots of growth phenomena
De Lauro, E.; De Martino, S.; De Siena, S.; Giorno, V.
2014-05-01
We show that the Gompertz equation describes the evolution in time of the median of a geometric stochastic process. Therefore, we induce that the process itself generates the growth. This result allows us further to exploit a stochastic variational principle to take account of self-regulation of growth through feedback of relative density variations. The conceptually well defined framework so introduced shows its usefulness by suggesting a form of control of growth by exploiting external actions.
Foliated stochastic calculus: Harmonic measures
Catuogno, Pedro J; Ruffino, Paulo R
2010-01-01
In this article we present an intrinsec construction of foliated Brownian motion via stochastic calculus adapted to foliation. The stochastic approach together with a proposed foliated vector calculus provide a natural method to work on harmonic measures. Other results include a decomposition of the Laplacian in terms of the foliated and basic Laplacians, a characterization of totally invariant measures and a differential equation for the density of harmonic measures.
Emerging non-volatile memories
Hong, Seungbum; Wouters, Dirk
2014-01-01
This book is an introduction to the fundamentals of emerging non-volatile memories and provides an overview of future trends in the field. Readers will find coverage of seven important memory technologies, including Ferroelectric Random Access Memory (FeRAM), Ferromagnetic RAM (FMRAM), Multiferroic RAM (MFRAM), Phase-Change Memories (PCM), Oxide-based Resistive RAM (RRAM), Probe Storage, and Polymer Memories. Chapters are structured to reflect diffusions and clashes between different topics. Emerging Non-Volatile Memories is an ideal book for graduate students, faculty, and professionals working in the area of non-volatile memory. This book also: Covers key memory technologies, including Ferroelectric Random Access Memory (FeRAM), Ferromagnetic RAM (FMRAM), and Multiferroic RAM (MFRAM), among others. Provides an overview of non-volatile memory fundamentals. Broadens readers' understanding of future trends in non-volatile memories.
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Steganalysis of stochastic modulation steganography
HE Junhui; HUANG Jiwu
2006-01-01
Stochastic modulation steganography embeds secret message within the cover image by adding stego-noise with a specific probabilistic distribution. No method is known to be applicable to the estimation of stochastic modulation steganography. By analyzing the distributions of the horizontal pixel difference of images before and after stochastic modulation embedding, we present a new steganalytic approach to accurately estimate the length of secret message in stochastic modulation steganography. The proposed method first establishes a model describing the statistical relationship among the differences of the cover image, stego-image and stego-noise. In the case of stego- image-only steganalysis, rough estimate of the distributional parameters of the cover image's pixel difference is obtained with the use of the provided stego-image. And grid search and Chi-square goodness of fit test are exploited to estimate the length of the secret message embedded with stochastic modulation steganography. The experimental results demonstrate that our new approach is effective for steganalyzing stochastic modulation steganography and accurately estimating the length of the secret message.
Governmentally amplified output volatility
Funashima, Yoshito
2016-11-01
Predominant government behavior is decomposed by frequency into several periodic components: updating cycles of infrastructure, Kuznets cycles, fiscal policy over business cycles, and election cycles. Little is known, however, about the theoretical impact of such cyclical behavior in public finance on output fluctuations. Based on a standard neoclassical growth model, this study intends to examine the frequency at which public investment cycles are relevant to output fluctuations. We find an inverted U-shaped relationship between output volatility and length of cycle in public investment. This implies that periodic behavior in public investment at a certain frequency range can cause aggravated output resonance. Moreover, we present an empirical analysis to test the theoretical implication, using the U.S. data in the period from 1968 to 2015. The empirical results suggest that such resonance phenomena change from low to high frequency.
Forecasting Multivariate Volatility using the VARFIMA Model on Realized Covariance Cholesky Factors
Halbleib, Roxana; Voev, Valeri
2011-01-01
This paper analyzes the forecast accuracy of the multivariate realized volatility model introduced by Chiriac and Voev (2010), subject to different degrees of model parametrization and economic evaluation criteria. Bymodelling the Cholesky factors of the covariancematrices, the model generates...... positive definite, but biased covariance forecasts. In this paper, we provide empirical evidence that parsimonious versions of the model generate the best covariance forecasts in the absence of bias correction. Moreover, we show by means of stochastic dominance tests that any risk averse investor...
Volatility Exposure for Strategic Asset Allocation
Briere, Marie; Burgues, Alexandre; Signori, Ombretta
2010-01-01
The authors examine the advantages of incorporating strategic exposure to equity volatility into the investment opportunity set of a long-term equity investor. They consider two standard volatility investments: implied volatility and volatility risk premium strategies. An analytical framework, which offers pragmatic solutions for long-term investors who seek exposure to volatility, is used to calibrate and assess the risk-return profiles of portfolios. The benefit of volatility exposure for a...
Grogan, Eric L.; Morris, John A.; Norris, Patrick R.; France, Daniel J.; Ozdas, Asli; Stiles, Renée A.; Harris, Paul A.; Dawant, Benoit M.; Speroff, Theodore
2004-01-01
Objective: To determine if using dense data capture to measure heart rate volatility (standard deviation) measured in 5-minute intervals predicts death. Background: Fundamental approaches to assessing vital signs in the critically ill have changed little since the early 1900s. Our prior work in this area has demonstrated the utility of densely sampled data and, in particular, heart rate volatility over the entire patient stay, for predicting death and prolonged ventilation. Methods: Approximately 120 million heart rate data points were prospectively collected and archived from 1316 trauma ICU patients over 30 months. Data were sampled every 1 to 4 seconds, stored in a relational database, linked to outcome data, and de-identified. HR standard deviation was continuously computed over 5-minute intervals (CVRD, cardiac volatility–related dysfunction). Logistic regression models incorporating age and injury severity score were developed on a test set of patients (N = 923), and prospectively analyzed in a distinct validation set (N = 393) for the first 24 hours of ICU data. Results: Distribution of CVRD varied by survival in the test set. Prospective evaluation of the model in the validation set gave an area in the receiver operating curve of 0.81 with a sensitivity and specificity of 70.1 and 80.0, respectively. CVRD predict death as early as 24 hours in the validation set. Conclusions: CVRD identifies a subgroup of patients with a high probability of dying. Death is predicted within first 24 hours of stay. We hypothesize CVRD is a surrogate for autonomic nervous system dysfunction. PMID:15319726
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Stacking with Stochastic Cooling
Caspers, Friedhelm
2004-01-01
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles seen by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly protected from the Schottky noise of the stack. Vice versa the stack has to be efficiently shielded against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 105, the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters)....
Stochastic Processes in Gravitropism
Yasmine eMeroz
2014-11-01
Full Text Available In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i {it dynamic sensing}, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification and integration of the signal. (ii The role of the cytoskeleton in signal-to-noise modulation and (iii in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
Brennan J. M.; Blaskiewicz, M.; Mernick, K.
2012-05-20
The full 6-dimensional [x,x'; y,y'; z,z'] stochastic cooling system for RHIC was completed and operational for the FY12 Uranium-Uranium collider run. Cooling enhances the integrated luminosity of the Uranium collisions by a factor of 5, primarily by reducing the transverse emittances but also by cooling in the longitudinal plane to preserve the bunch length. The components have been deployed incrementally over the past several runs, beginning with longitudinal cooling, then cooling in the vertical planes but multiplexed between the Yellow and Blue rings, next cooling both rings simultaneously in vertical (the horizontal plane was cooled by betatron coupling), and now simultaneous horizontal cooling has been commissioned. The system operated between 5 and 9 GHz and with 3 x 10{sup 8} Uranium ions per bunch and produces a cooling half-time of approximately 20 minutes. The ultimate emittance is determined by the balance between cooling and emittance growth from Intra-Beam Scattering. Specific details of the apparatus and mathematical techniques for calculating its performance have been published elsewhere. Here we report on: the method of operation, results with beam, and comparison of results to simulations.
Adaptation in stochastic environments
Clark, Colib
1993-01-01
The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "Cha...
Kallianpur, Gopinath; Hida, Takeyuki
1987-01-01
The use of probabilistic methods in the biological sciences has been so well established by now that mathematical biology is regarded by many as a distinct dis cipline with its own repertoire of techniques. The purpose of the Workshop on sto chastic methods in biology held at Nagoya University during the week of July 8-12, 1985, was to enable biologists and probabilists from Japan and the U. S. to discuss the latest developments in their respective fields and to exchange ideas on the ap plicability of the more recent developments in stochastic process theory to problems in biology. Eighteen papers were presented at the Workshop and have been grouped under the following headings: I. Population genetics (five papers) II. Measure valued diffusion processes related to population genetics (three papers) III. Neurophysiology (two papers) IV. Fluctuation in living cells (two papers) V. Mathematical methods related to other problems in biology, epidemiology, population dynamics, etc. (six papers) An important f...
Turbulence and Stochastic Processes
Celani, Antonio; Mazzino, Andrea; Pumir, Alain
sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.
AA, stochastic precooling kicker
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling", while a shutter shielded the deeply cooled antiproton stack from the violent action of the precooling kicker. In this picture, the injection orbit is to the left, the stack orbit to the far right, the separating shutter is in open position. After several seconds of precooling (in momentum and in the vertical plane), the shutter was opened briefly, so that by means of RF the precooled antiprotons could be transferred to the stack tail, where they were subjected to further cooling in momentum and both transverse planes, until they ended up, deeply cooled, in the stack core. The fast shutter, which had to open and close in a fraction of a second was an essential item of the cooling scheme and a mechanical masterpiece. Here the shutter is in the open position. The precooling pickups were of the same design, with the difference that the kickers had cooling circuits and the pickups not. 8401150 shows a precooling pickup with the shutte...
Bulsara, Adi R., E-mail: bulsara@spawar.navy.mil [SPAWAR Systems Center Pacific, San Diego, CA 92152-5001 (United States); Dari, Anna, E-mail: adari@asu.edu [Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287-9309 (United States); Ditto, William L., E-mail: william.ditto@asu.edu [Ira A. Fulton School of Engineering, Arizona State University, Tempe, AZ 85287-9309 (United States); Murali, K., E-mail: kmurali@annauniv.edu [Department of Physics, Anna University, Chennai 600 025 (India); Sinha, Sudeshna, E-mail: sudeshna@imsc.res.in [Institute of Mathematical Sciences, Taramani, Chennai 600 113 (India); Indian Institute of Science Education and Research, Mohali, Transit Campus: MGSIPAP Complex, Sector 26 Chandigarh (India)
2010-10-05
In a recent publication it was shown that, when one drives a two-state system with two square waves as input, the response of the system mirrors a logical output (NOR/OR). The probability of obtaining the correct logic response is controlled by the interplay between the noise-floor and the nonlinearity. As one increases the noise intensity, the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Varying the nonlinearity (or the thresholds) of the system allows one to morph the output into another logic operation (NAND/AND) whose probability displays analogous behavior. Thus, the outcome of the interplay of nonlinearity and noise is a flexible logic gate with enhanced performance. Here we review this concept of 'Logical Stochastic Resonance' (LSR) and provide details of an electronic circuit system demonstrating LSR. Our proof-of-principle experiment involves a particularly simple realization of a two-state system realized by two adjustable thresholds. We also review CMOS implementations of a simple LSR circuit, and the concatenation of these LSR modules to emulate combinational logic, such as data flip-flop and full adder operations.
Segmentation of stochastic images with a stochastic random walker method.
Pätz, Torben; Preusser, Tobias
2012-05-01
We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.
General N-th Degree Stochastic Dominance
张顺明
2001-01-01
This paper examines N-th degree stochastic dominance which isused to compare the risk factor of risky assets after summarizing the definitions of first degree stochastic dominance and second degree stochastic dominance. The paper defines general N-th degree stochastic dominance, presents a sufficient and necessary condition which is the equivalent theorem of general N-th degree stochastic dominance. The feasible utility form is constructed to explain the economic meaning of N-th degree stochastic dominance in the field of financial economics. The equivalent condition is described by the probability distribution functions of risky assets, which are not related to utility functions (preference relations).
Stability Analysis for Stochastic Optimization Problems
无
2007-01-01
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
A Stochastic Collocation Algorithm for Uncertainty Analysis
Mathelin, Lionel; Hussaini, M. Yousuff; Zang, Thomas A. (Technical Monitor)
2003-01-01
This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Stochastic simulation in systems biology.
Székely, Tamás; Burrage, Kevin
2014-11-01
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Tsionas, Mike G.; Michaelides, Panayotis G.
2017-09-01
We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by traditional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014, by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data (;neglected chaos;).
On forecasting Exchange Rate Volatility.
Hafner, Christian
2003-01-01
In an efficient market, foreign exchange rates have to guarantee absence of triangular arbitrage. This note shows that the no-arbitrage condition can be exploited for forecasting the volatility of a single rate by using the information contained in the other rates. Linearly transforming the volatility forecasts of a bivariate model is shown to be more efficient than using a univariate model for the cross-rate.
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian
2013-01-01
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional SP simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic SP replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on th...
Stochastic models for atmospheric dispersion
Ditlevsen, Ove Dalager
2003-01-01
Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... dependent particle velocity into a position independent Gaussian velocity. Boundary conditions are obtained from Itos rule of stochastic differentiation. The model directly point at a canonical rule of reflection for the approximating random walk with finite time step. This reflection rule is different from...
Intrinsic optimization using stochastic nanomagnets
Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo
2017-01-01
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053
Mechanical autonomous stochastic heat engines
Serra-Garcia, Marc; Foehr, Andre; Moleron, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara; . Team
Stochastic heat engines extract work from the Brownian motion of a set of particles out of equilibrium. So far, experimental demonstrations of stochastic heat engines have required extreme operating conditions or nonautonomous external control systems. In this talk, we will present a simple, purely classical, autonomous stochastic heat engine that uses the well-known tension induced nonlinearity in a string. Our engine operates between two heat baths out of equilibrium, and transfers energy from the hot bath to a work reservoir. This energy transfer occurs even if the work reservoir is at a higher temperature than the hot reservoir. The talk will cover a theoretical investigation and experimental results on a macroscopic setup subject to external noise excitations. This system presents an opportunity for the study of non equilibrium thermodynamics and is an interesting candidate for innovative energy conversion devices.
Principal axes for stochastic dynamics.
Vasconcelos, V V; Raischel, F; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-09-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Stochastic models of cell motility
Gradinaru, Cristian
2012-01-01
Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...
Correlation functions in stochastic inflation
Vennin, Vincent [University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth (United Kingdom); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow (Russian Federation); Utrecht University, Department of Physics and Astronomy, Institute for Theoretical Physics, Utrecht (Netherlands)
2015-09-15
Combining the stochastic and δ N formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and we comment on the physical implications of this effect. (orig.)
Principal axes for stochastic dynamics
Vasconcelos, V V; Haase, M; Peinke, J; Wächter, M; Lind, P G; Kleinhans, D
2011-01-01
We introduce a general procedure for directly ascertaining how many independent stochastic sources exist in a complex system modeled through a set of coupled Langevin equations of arbitrary dimension. The procedure is based on the computation of the eigenvalues and the corresponding eigenvectors of local diffusion matrices. We demonstrate our algorithm by applying it to two examples of systems showing Hopf-bifurcation. We argue that computing the eigenvectors associated to the eigenvalues of the diffusion matrix at local mesh points in the phase space enables one to define vector fields of stochastic eigendirections. In particular, the eigenvector associated to the lowest eigenvalue defines the path of minimum stochastic forcing in phase space, and a transform to a new coordinate system aligned with the eigenvectors can increase the predictability of the system.
Applied probability and stochastic processes
Sumita, Ushio
1999-01-01
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability i...
Fundamentals of stochastic nature sciences
Klyatskin, Valery I
2017-01-01
This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under wh...
Stacking with stochastic cooling
Caspers, Fritz E-mail: Fritz.Caspers@cern.ch; Moehl, Dieter
2004-10-11
Accumulation of large stacks of antiprotons or ions with the aid of stochastic cooling is more delicate than cooling a constant intensity beam. Basically the difficulty stems from the fact that the optimized gain and the cooling rate are inversely proportional to the number of particles 'seen' by the cooling system. Therefore, to maintain fast stacking, the newly injected batch has to be strongly 'protected' from the Schottky noise of the stack. Vice versa the stack has to be efficiently 'shielded' against the high gain cooling system for the injected beam. In the antiproton accumulators with stacking ratios up to 10{sup 5} the problem is solved by radial separation of the injection and the stack orbits in a region of large dispersion. An array of several tapered cooling systems with a matched gain profile provides a continuous particle flux towards the high-density stack core. Shielding of the different systems from each other is obtained both through the spatial separation and via the revolution frequencies (filters). In the 'old AA', where the antiproton collection and stacking was done in one single ring, the injected beam was further shielded during cooling by means of a movable shutter. The complexity of these systems is very high. For more modest stacking ratios, one might use azimuthal rather than radial separation of stack and injected beam. Schematically half of the circumference would be used to accept and cool new beam and the remainder to house the stack. Fast gating is then required between the high gain cooling of the injected beam and the low gain stack cooling. RF-gymnastics are used to merge the pre-cooled batch with the stack, to re-create free space for the next injection, and to capture the new batch. This scheme is less demanding for the storage ring lattice, but at the expense of some reduction in stacking rate. The talk reviews the 'radial' separation schemes and also gives some
Lacksonen, Thomas A.
1994-01-01
Small space flight project design at NASA Langley Research Center goes through a multi-phase process from preliminary analysis to flight operations. The process insures that each system achieves its technical objectives with demonstrated quality and within planned budgets and schedules. A key technical component of early phases is decision analysis, which is a structure procedure for determining the best of a number of feasible concepts based upon project objectives. Feasible system concepts are generated by the designers and analyzed for schedule, cost, risk, and technical measures. Each performance measure value is normalized between the best and worst values and a weighted average score of all measures is calculated for each concept. The concept(s) with the highest scores are retained, while others are eliminated from further analysis. This project automated and enhanced the decision analysis process. Automation of the decision analysis process was done by creating a user-friendly, menu-driven, spreadsheet macro based decision analysis software program. The program contains data entry dialog boxes, automated data and output report generation, and automated output chart generation. The enhancements to the decision analysis process permit stochastic data entry and analysis. Rather than enter single measure values, the designers enter the range and most likely value for each measure and concept. The data can be entered at the system or subsystem level. System level data can be calculated as either sum, maximum, or product functions of the subsystem data. For each concept, the probability distributions are approximated for each measure and the total score for each concept as either constant, triangular, normal, or log-normal distributions. Based on these distributions, formulas are derived for the probability that the concept meets any given constraint, the probability that the concept meets all constraints, and the probability that the concept is within a given
When greediness fails: examples from stochastic scheduling
Uetz, Marc Jochen
The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.
When greediness fails: examples from stochastic scheduling
Uetz, Marc
2003-01-01
The purpose of this paper is to present examples for the sometimes surprisingly different behavior of deterministic and stochastic scheduling problems. In particular, it demonstrates some seemingly counterintuitive properties of optimal scheduling policies for stochastic machine scheduling problems.
Transport properties of stochastic Lorentz models
Beijeren, H. van
1982-01-01
Diffusion processes are considered for one-dimensional stochastic Lorentz models, consisting of randomly distributed fixed scatterers and one moving light particle. In waiting time Lorentz models the light particle makes instantaneous jumps between scatterers after a stochastically distributed waiti
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Stochastic methods in quantum mechanics
Gudder, Stanley P
2005-01-01
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
Stochastic epidemic models: a survey
Britton, Tom
2009-01-01
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Stochastic and infinite dimensional analysis
Carpio-Bernido, Maria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria; Silva, José
2016-01-01
This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Schwinger Mechanism with Stochastic Quantization
Fukushima, Kenji
2014-01-01
We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive the Schwinger mechanism under a time-dependent electric field. We also discuss a physical interpretation with help of numerical simulations and develop an analogue to the one-dimensional scattering with the non-relativistic Schroedinger equation. We can then reformulate the Schwinger mechanism as the high-energy quantum reflection problem rather than tunneling.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
QB1 - Stochastic Gene Regulation
Munsky, Brian [Los Alamos National Laboratory
2012-07-23
Summaries of this presentation are: (1) Stochastic fluctuations or 'noise' is present in the cell - Random motion and competition between reactants, Low copy, quantization of reactants, Upstream processes; (2) Fluctuations may be very important - Cell-to-cell variability, Cell fate decisions (switches), Signal amplification or damping, stochastic resonances; and (3) Some tools are available to mode these - Kinetic Monte Carlo simulations (SSA and variants), Moment approximation methods, Finite State Projection. We will see how modeling these reactions can tell us more about the underlying processes of gene regulation.
Algebraic and stochastic coding theory
Kythe, Dave K
2012-01-01
Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.
Stochastic Kinetics of Nascent RNA
Xu, Heng; Skinner, Samuel O.; Sokac, Anna Marie; Golding, Ido
2016-09-01
The stochastic kinetics of transcription is typically inferred from the distribution of RNA numbers in individual cells. However, cellular RNA reflects additional processes downstream of transcription, hampering this analysis. In contrast, nascent (actively transcribed) RNA closely reflects the kinetics of transcription. We present a theoretical model for the stochastic kinetics of nascent RNA, which we solve to obtain the probability distribution of nascent RNA per gene. The model allows us to evaluate the kinetic parameters of transcription from single-cell measurements of nascent RNA. The model also predicts surprising discontinuities in the distribution of nascent RNA, a feature which we verify experimentally.
The dynamics of stochastic processes
Basse-O'Connor, Andreas
In the present thesis the dynamics of stochastic processes is studied with a special attention to the semimartingale property. This is mainly motivated by the fact that semimartingales provide the class of the processes for which it is possible to define a reasonable stochastic calculus due...... average processes, and when the driving process is a Lévy or a chaos process the semimartingale property is characterized in the filtration spanned by the driving process and in the natural filtration when the latter is a Brownian motion. To obtain some of the above results an integrability of seminorm...
Stochastic model in microwave propagation
Ranfagni, A. [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy); Mugnai, D., E-mail: d.mugnai@ifac.cnr.it [“Nello Carrara” Institute of Applied Physics, CNR Florence Research Area, Via Madonna del Piano 10, 50019 Sesto Fiorentino (Italy)
2011-11-28
Further experimental results of delay time in microwave propagation are reported in the presence of a lossy medium (wood). The measurements show that the presence of a lossy medium makes the propagation slightly superluminal. The results are interpreted on the basis of a stochastic (or path integral) model, showing how this model is able to describe each kind of physical system in which multi-path trajectories are present. -- Highlights: ► We present new experimental results on electromagnetic “anomalous” propagation. ► We apply a path integral theoretical model to wave propagation. ► Stochastic processes and multi-path trajectories in propagation are considered.
Stochastic Model Checking of the Stochastic Quality Calculus
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input...
Observability Estimate for Stochastic Schroedinger Equations
2012-01-01
In this paper, we establish a boundary observability estimate for stochastic Schr\\"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr\\"{o}dinger-like operator. Applications to the state observation problem for semilinear stochastic Schr\\"{o}dinger equations and the unique continuation problem for stochastic Schr\\"{o}dinger equations are also addressed.
Transport in a stochastic magnetic field
White, R.B.; Wu, Yanlin [Princeton Univ., NJ (United States). Plasma Physics Lab.; Rax, J.M. [Association Euratom-CEA, Centre d`Etudes Nucleaires de Cadarache, 13 -Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee
1992-09-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Transport in a stochastic magnetic field
White, R.B.; Wu, Yanlin (Princeton Univ., NJ (United States). Plasma Physics Lab.); Rax, J.M. (Association Euratom-CEA, Centre d' Etudes Nucleaires de Cadarache, 13 -Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee)
1992-01-01
Collisional heat transport in a stochastic magnetic field configuration is investigated. Well above stochastic threshold, a numerical solution of a Chirikov-Taylor model shows a short-time nonlocal regime, but at large time the Rechester-Rosenbluth effective diffusion is confirmed. Near stochastic threshold, subdiffusive behavior is observed for short mean free paths. The nature of this subdiffusive behavior is understood in terms of the spectrum of islands in the stochastic sea.
Stochastic modeling and analysis of telecoms networks
Decreusefond, Laurent
2012-01-01
This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an
Exact Algorithms for Solving Stochastic Games
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels;
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
Recent Advances in Volatiles of Teas
Xin-Qiang Zheng
2016-03-01
Full Text Available Volatile compounds are important components of tea aroma, a key attribute of sensory quality. The present review examines the formation of aromatic volatiles of various kinds of teas and factors influencing the formation of tea volatiles, including tea cultivar, growing environment and agronomic practices, processing method and storage of tea. The determination of tea volatiles and the relationship of active-aroma volatiles with the sensory qualities of tea are also discussed in the present paper.
Michta, Mariusz
2017-02-01
In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations with respect to semimartingale integrators. We present new connections between their solutions. In particular, we show that attainable sets of solutions to stochastic inclusions are subsets of values of multivalued solutions of certain set-valued stochastic equations. We also show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. The results obtained in the paper generalize results dealing with this topic known both in deterministic and stochastic cases.
EDITORIAL: Stochasticity in fusion plasmas Stochasticity in fusion plasmas
Unterberg, Bernhard
2010-03-01
Structure formation and transport in stochastic plasmas is a topic of growing importance in many fields of plasma physics from astrophysics to fusion research. In particular, the possibility to control transport in the boundary of confined fusion plasmas by resonant magnetic perturbations has been investigated extensively during recent years. A major research achievement was finding that the intense transient particle and heat fluxes associated with edge localized modes (here type-I ELMs) in magnetically confined fusion plasmas can be mitigated or even suppressed by resonant magnetic perturbation fields. This observation opened up a possible scheme to avoid too large erosion and material damage by such transients in future fusion devices such as ITER. However, it is widely recognized that a more basic understanding is needed to extrapolate the results obtained in present experiments to future fusion devices. The 4th workshop on Stochasticity in Fusion Plasmas was held in Jülich, Germany, from 2 to 4 March 2009. This series of workshops aims at gathering fusion experts from various plasma configurations such as tokamaks, stellarators and reversed field pinches to exchange knowledge on structure formation and transport in stochastic fusion plasmas. The workshops have attracted colleagues from both experiment and theory and stimulated fruitful discussions about the basics of stochastic fusion plasmas. Important papers from the first three workshops in 2003, 2005 and 2007 have been published in previous special issues of Nuclear Fusion (stacks.iop.org/NF/44/i=6, stacks.iop.org/NF/46/i=4 and stacks.iop.org/NF/48/i=2). This special issue comprises contributions presented at the 4th SFP workshop, dealing with the main subjects such as formation of stochastic magnetic layers, energy and particle transport in stochastic magnetic fields, plasma response to external, non-axis-symmetric perturbations and last but not least application of resonant magnetic perturbations for
Variational principles for stochastic soliton dynamics.
Holm, Darryl D; Tyranowski, Tomasz M
2016-03-01
We develop a variational method of deriving stochastic partial differential equations whose solutions follow the flow of a stochastic vector field. As an example in one spatial dimension, we numerically simulate singular solutions (peakons) of the stochastically perturbed Camassa-Holm (CH) equation derived using this method. These numerical simulations show that peakon soliton solutions of the stochastically perturbed CH equation persist and provide an interesting laboratory for investigating the sensitivity and accuracy of adding stochasticity to finite dimensional solutions of stochastic partial differential equations. In particular, some choices of stochastic perturbations of the peakon dynamics by Wiener noise (canonical Hamiltonian stochastic deformations, CH-SD) allow peakons to interpenetrate and exchange order on the real line in overtaking collisions, although this behaviour does not occur for other choices of stochastic perturbations which preserve the Euler-Poincaré structure of the CH equation (parametric stochastic deformations, P-SD), and it also does not occur for peakon solutions of the unperturbed deterministic CH equation. The discussion raises issues about the science of stochastic deformations of finite-dimensional approximations of evolutionary partial differential equation and the sensitivity of the resulting solutions to the choices made in stochastic modelling.
Symmetrized solutions for nonlinear stochastic differential equations
G. Adomian
1981-01-01
Full Text Available Solutions of nonlinear stochastic differential equations in series form can be put into convenient symmetrized forms which are easily calculable. This paper investigates such forms for polynomial nonlinearities, i.e., equations of the form Ly+ym=x where x is a stochastic process and L is a linear stochastic operator.
Stochastic Programming with Simple Integer Recourse
Louveaux, François V.; van der Vlerk, Maarten H.
1993-01-01
Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic c
Symmetry reduction for stochastic hybrid systems
Bujorianu, L.M.; Katoen, J.P.
2009-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. We first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Then, we genera
Symmetry Reduction For Stochastic Hybrid Systems
Bujorianu, L.M.; Katoen, J.P.
2008-01-01
This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA). Th
Models and algorithms for stochastic online scheduling
Megow, N.; Uetz, Marc Jochen; Vredeveld, T.
We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that
Stability of stochastic switched SIRS models
Meng, Xiaoying; Liu, Xinzhi; Deng, Feiqi
2011-11-01
Stochastic stability problems of a stochastic switched SIRS model with or without distributed time delay are considered. By utilizing the Lyapunov methods, sufficient stability conditions of the disease-free equilibrium are established. Stability conditions about the subsystem of the stochastic switched SIRS systems are also obtained.
Stochastic nonlinear differential equations. I
Heilmann, O.J.; Kampen, N.G. van
1974-01-01
A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these co
Stochastic Modelling of Energy Systems
Andersen, Klaus Kaae
2001-01-01
equations are expressed in terms of stochastic differential equations. From a theoretical viewpoint the techniques for experimental design, parameter estimation and model validation are considered. From the practical viewpoint emphasis is put on how this methods can be used to construct models adequate...
Stochastic Modelling of River Geometry
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models...
The bicriterion stochastic knapsack problem
Andersen, Kim Allan
We discuss the bicriterion stochastic knapsack problem. It is described as follows. We have a known capacity of some resource, and a finite set of projects. Each project requires some units of the resource which is not known in advance, but given by a discrete probability distribution with a finite...
Stochastic Processes in Epidemic Theory
Lefèvre, Claude; Picard, Philippe
1990-01-01
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
Stochastic-field cavitation model
Dumond, J., E-mail: julien.dumond@areva.com [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen (Germany); Magagnato, F. [Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstrasse 12, D-76131 Karlsruhe (Germany); Class, A. [AREVA Nuclear Professional School, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany); Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen (Germany)
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-01
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost P.; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution
Model checking mobile stochastic logic.
De Nicola, Rocco; Katoen, Joost-Pieter; Latella, Diego; Loreti, Michele; Massink, Mieke
2007-01-01
The Temporal Mobile Stochastic Logic (MOSL) has been introduced in previous work by the authors for formulating properties of systems specified in STOKLAIM, a Markovian extension of KLAIM. The main purpose of MOSL is to address key functional aspects of global computing such as distribution awarenes
Stochastic resin transfer molding process
Park, M
2016-01-01
We consider one-dimensional and two-dimensional models of stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in the two-dimensional case. We show how variability of time to fill depends on correlation lengths and smoothness of a random permeability field.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Stochastic Subspace Modelling of Turbulence
Sichani, Mahdi Teimouri; Pedersen, B. J.; Nielsen, Søren R.K.
2009-01-01
Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper...
Stochastic arbitrage return and its implication for option pricing
Fedotov, Sergei; Panayides, Stephanos
2005-01-01
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility “smile” can also be explained in terms of random arbitrage opportunities.
Spiral mining for lunar volatiles
Schmitt, H. H.; Kulcinski, G. L.; Sviatoslavsky, I. N.; Carrier, W. D., III
Lunar spiral mining, extending outward from a periodically mobile central power and processing station represents an alternative for comparison with more traditional mining schemes. In this concept, a mining machine would separate regolith fines and extract the contained volatiles. Volatiles then would be pumped along the miner's support arm to the central station for refining and for export or storage. The basic architecture of the central processing station would be cylindrical. A central core area could house the power subsystem of hydrogen-oxygen engines or fuel cells. Habitat sections and other crew occupied areas could be arranged around the power generation core. The outer cylinder could include all volatile refining subsystems. Solar thermal power collectors and reflectors would be positioned on top of the central station. Long term exploitation of a volatile resource region would begin with establishment of a support base at the center of a long boundary of the region. The mining tract for each spiral mining system would extend orthogonal to this boundary. New spiral mining systems would be activated along parallel tracts as demand for lunar He-3 and other solar wind volatiles increased.
Stochastic averaging of quasi-Hamiltonian systems
朱位秋
1996-01-01
A stochastic averaging method is proposed for quasi-Hamiltonian systems (Hamiltonian systems with light dampings subject to weakly stochastic excitations). Various versions of the method, depending on whether the associated Hamiltonian systems are integrable or nonintegrable, resonant or nonresonant, are discussed. It is pointed out that the standard stochastic averaging method and the stochastic averaging method of energy envelope are special cases of the stochastic averaging method of quasi-Hamiltonian systems and that the results obtained by this method for several examples prove its effectiveness.
Research on nonlinear stochastic dynamical price model
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
RICE PRICE VOLATILITY IN EAST JAVA
Wati R.Y.E.
2017-09-01
Full Text Available The purpose of the research is analyzing the volatility and volatility spillover of monthly price of paddy at the level of farmers and consumers in 2010-2016. ARCH/GARCH used to analyze volatility and GARCH BEKK-model is used to analyze the volatility spillover. The results of the analysis show that price volatility at the farmer level is very high (extremely high volatility, price volatility at the consumer level is low (low volatility, and volatility spillover does not occur between the farmers and the consumers market. The need to guarantee an effective floor price as well as information disclosure related to the market commodity prices so that the pattern of prices transmission among interrelated markets can be symmetrical.
The price of fixed income market volatility
Mele, Antonio
2015-01-01
Fixed income volatility and equity volatility evolve heterogeneously over time, co-moving disproportionately during periods of global imbalances and each reacting to events of different nature. While the methodology for options-based "model-free" pricing of equity volatility has been known for some time, little is known about analogous methodologies for pricing various fixed income volatilities. This book fills this gap and provides a unified evaluation framework of fixed income volatility while dealing with disparate markets such as interest-rate swaps, government bonds, time-deposits and credit. It develops model-free, forward looking indexes of fixed-income volatility that match different quoting conventions across various markets, and uncovers subtle yet important pitfalls arising from naïve superimpositions of the standard equity volatility methodology when pricing various fixed income volatilities. The ultimate goal of the authors´ efforts is to make interest rate volatility standardization a valuable...
Understanding volatility dynamics in the EU-ETS market
Sanin, Maria Eugenia; Mansanet-Bataller, Maria; Violante, Francesco
We study the short-term price behavior of Phase 2 EU emission allowances. We model returns and volatility dynamics, and we demonstrate that a standard ARMAX-GARCH framework is inadequate for this modeling and that the gaussianity assumption is rejected due to a number of outliers. To improve...... the fitness of the model, we combine the underlying price process with an additive stochastic jump process. We improve the model's performance by introducing a time-varying jump probability that is explained by two variables: the daily relative change in the volume of transactions and the European Commission...... periods. Thus, authorities face a trade off between disseminating information effectively and promoting market stability....
Stochastic Reachability Analysis of Hybrid Systems
Bujorianu, Luminita Manuela
2012-01-01
Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then...
Stochastic Analysis : A Series of Lectures
Dozzi, Marco; Flandoli, Franco; Russo, Francesco
2015-01-01
This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields o...
Observability of market daily volatility
Petroni, Filippo; Serva, Maurizio
2016-02-01
We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 to 2014. We show that it is possible to define a Daily Market Volatility σ(t) which is directly observable from data. This quantity is usually indirectly defined by r(t) = σ(t) ω(t) where the r(t) are the daily returns of the market index and the ω(t) are i.i.d. random variables with vanishing average and unitary variance. The relation r(t) = σ(t) ω(t) alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.
Consistent ranking of volatility models
Hansen, Peter Reinhard; Lunde, Asger
2006-01-01
result in an inferior model being chosen as "best" with a probability that converges to one as the sample size increases. We document the practical relevance of this problem in an empirical application and by simulation experiments. Our results provide an additional argument for using the realized...... variance in out-of-sample evaluations rather than the squared return. We derive the theoretical results in a general framework that is not specific to the comparison of volatility models. Similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable.......We show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility. For example, the substitution of a squared return for the conditional variance in the evaluation of ARCH-type models can...
Oil Volatility Risk and Expected Stock Returns
Christoffersen, Peter; Pan, Xuhui (Nick)
After the financialization of commodity futures markets in 2004-05 oil volatility has become a strong predictor of returns and volatility of the overall stock market. Furthermore, stocks' exposure to oil volatility risk now drives the cross-section of expected returns. The difference in average...... return between the quintile of stocks with low exposure and high exposure to oil volatility is significant at 0.66% per month, and oil volatility risk carries a significant risk premium of -0.60% per month. In the post-financialization period, oil volatility risk is strongly related with various measures...
Rhenium volatilization in waste glasses
Xu, Kai; Pierce, David A. [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Hrma, Pavel, E-mail: pavel.hrma@pnnl.gov [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Schweiger, Michael J. [Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Kruger, Albert A. [U.S. Department of Energy, Office of River Protection, Richland, WA 99352 (United States)
2015-09-15
Highlights: • Re did not volatilize from a HLW feed until 1000 °C. • Re began to volatilize from LAW feeds at ∼600 °C. • The vigorous foaming and generation of gases from salts enhanced Re evaporation in LAW feeds. • The HLW glass with less foaming and salts is a promising medium for Tc immobilization. - Abstract: We investigated volatilization of rhenium (Re), sulfur, cesium, and iodine during the course of conversion of high-level waste melter feed to glass and compared the results for Re volatilization with those in low-activity waste borosilicate glasses. Whereas Re did not volatilize from high-level waste feed heated at 5 K min{sup −1} until 1000 °C, it began to volatilize from low-activity waste borosilicate glass feeds at ∼600 °C, a temperature ∼200 °C below the onset temperature of evaporation from pure KReO{sub 4}. Below 800 °C, perrhenate evaporation in low-activity waste melter feeds was enhanced by vigorous foaming and generation of gases from molten salts as they reacted with the glass-forming constituents. At high temperatures, when the glass-forming phase was consolidated, perrhenates were transported to the top surface of glass melt in bubbles, typically together with sulfates and halides. Based on the results of this study (to be considered preliminary at this stage), the high-level waste glass with less foaming and salts appears a promising medium for technetium immobilization.
Ruin problems with stochastic premium stochastic return on investments
WANG Rongming; XU Lin; YAO Dingjun
2007-01-01
In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro- differential equations for the expected discounted penalty function are ob- tained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper.
Factors affecting the volatilization of volatile organic compounds from wastewater
Junya Intamanee
2006-09-01
Full Text Available This study aimed to understand the influence of the wind speed (U10cm, water depth (h and suspended solids (SS on mass transfer coefficient (KOLa of volatile organic compounds (VOCs volatilized from wastewater. The novelty of this work is not the method used to determine KOLa but rather the use of actual wastewater instead of pure water as previously reported. The influence of U10cm, h, and SS on KOLa was performed using a volatilization tank with the volume of 100-350 L. Methyl Ethyl Ketone (MEK was selected as a representative of VOCs investigated here in. The results revealed that the relationship between KOLa and the wind speeds falls into two regimes with a break at the wind speed of 2.4 m/s. At U10cm 2.4 m/s, KOLa increased more rapidly. The relationship between KOLa and U10cm was also linear but has a distinctly higher slope. For the KOLa dependency on water depth, the KOLa decreased significantly with increasing water depth up to a certain water depth after that the increase in water depth had small effect on KOLa. The suspended solids in wastewater also played an important role on KOLa. Increased SS resulted in a significant reduction of KOLa over the investigated range of SS. Finally, the comparison between KOLa obtained from wastewater and that of pure water revealed that KOLa from wastewater were much lower than that of pure water which was pronounced at high wind speed and at small water depth. This was due the presence of organic mass in wastewater which provided a barrier to mass transfer and reduced the degree of turbulence in the water body resulting in low volatilization rate and thus KOLa. From these results, the mass transfer model for predicting VOCs emission from wastewater should be developed based on the volatilization of VOCs from wastewater rather than that from pure water.
Stochastic integration and differential equations
Protter, Philip E
2003-01-01
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...
Optical stochastic cooling in Tevatron
Lebedev, V
2012-01-01
Intrabeam scattering is the major mechanism resulting in a growth of beam emittances and fast luminosity degradation in the Tevatron. As a result in the case of optimal collider operation only about 40% of antiprotons are used to the store end and the rest are discarded. Beam cooling is the only effective remedy to increase the particle burn rate and, consequently, the luminosity. Unfortunately neither electron nor stochastic cooling can be effective at the Tevatron energy and bunch density. Thus the optical stochastic cooling (OSC) is the only promising technology capable to cool the Tevatron beam. Possible ways of such cooling implementation in the Tevatron and advances in the OSC cooling theory are discussed in this paper. The technique looks promising and potentially can double the average Tevatron luminosity without increasing its peak value and the antiproton production.
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Stochastic Modeling of Soil Salinity
Suweis, S; Van der Zee, S E A T M; Daly, E; Maritan, A; Porporato, A; 10.1029/2010GL042495
2012-01-01
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long-term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in long-term soil salinization trend...
Stochastic Vehicle Routing with Recourse
Goertz, Inge Li; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Self-Organising Stochastic Encoders
Luttrell, Stephen
2010-01-01
The processing of mega-dimensional data, such as images, scales linearly with image size only if fixed size processing windows are used. It would be very useful to be able to automate the process of sizing and interconnecting the processing windows. A stochastic encoder that is an extension of the standard Linde-Buzo-Gray vector quantiser, called a stochastic vector quantiser (SVQ), includes this required behaviour amongst its emergent properties, because it automatically splits the input space into statistically independent subspaces, which it then separately encodes. Various optimal SVQs have been obtained, both analytically and numerically. Analytic solutions which demonstrate how the input space is split into independent subspaces may be obtained when an SVQ is used to encode data that lives on a 2-torus (e.g. the superposition of a pair of uncorrelated sinusoids). Many numerical solutions have also been obtained, using both SVQs and chains of linked SVQs: (1) images of multiple independent targets (encod...
Stochastic problems in population genetics
Maruyama, Takeo
1977-01-01
These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura...
Stochastic vehicle routing with recourse
Gørtz, Inge Li; Nagarajan, Viswanath; Saket, Rishi
2012-01-01
We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand...... instantiations, a recourse route is computed - but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular...... orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based ω(1) hardness of approximation for StochVRP, even on star-like metrics on which our...
Modeling the Volatility in Global Fertilizer Prices
P-Y. Chen (Ping-Yu); C-L. Chang (Chia-Lin); C-C. Chen (Chi-Chung); M.J. McAleer (Michael)
2010-01-01
textabstractThe main purpose of this paper is to estimate the volatility in global fertilizer prices. The endogenous structural breakpoint unit root test and alternative volatility models, including the generalized autoregressive conditional heteroskedasticity (GARCH) model, Exponential GARCH (EGARC
Fluctuation behaviors of financial return volatility duration
Niu, Hongli; Wang, Jun; Lu, Yunfan
2016-04-01
It is of significantly crucial to understand the return volatility of financial markets because it helps to quantify the investment risk, optimize the portfolio, and provide a key input of option pricing models. The characteristics of isolated high volatility events above certain threshold in price fluctuations and the distributions of return intervals between these events arouse great interest in financial research. In the present work, we introduce a new concept of daily return volatility duration, which is defined as the shortest passage time when the future volatility intensity is above or below the current volatility intensity (without predefining a threshold). The statistical properties of the daily return volatility durations for seven representative stock indices from the world financial markets are investigated. Some useful and interesting empirical results of these volatility duration series about the probability distributions, memory effects and multifractal properties are obtained. These results also show that the proposed stock volatility series analysis is a meaningful and beneficial trial.
Non-Gaussian Stochastic Gravity
Bates, Jason D.
2013-01-01
This paper presents a new, non-Gaussian formulation of stochastic gravity by incorporating the higher moments of the fluctuations of the quantum stress energy tensor for a free quantum scalar field in a consistent way. A scheme is developed for obtaining realizations of these fluctuations in terms of the Wightman function, and the behavior of the fluctuations is investigated. The resulting probability distribution for fluctuations of the energy density in Minkowski spacetime is found to be si...
Stochastic processes and filtering theory
Jazwinski, Andrew H
2007-01-01
This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well.Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probab
Stochastic Gravity: Theory and Applications
Hu Bei Lok
2008-05-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out
Stochastic control of traffic patterns
Gaididei, Yuri B.; Gorria, Carlos; Berkemer, Rainer
2013-01-01
A stochastic modulation of the safety distance can reduce traffic jams. It is found that the effect of random modulation on congestive flow formation depends on the spatial correlation of the noise. Jam creation is suppressed for highly correlated noise. The results demonstrate the advantage...... of heterogeneous performance of the drivers in time as well as individually. This opens the possibility for the construction of technical tools to control traffic jam formation....
Foundations of infinitesimal stochastic analysis
Stroyan, KD
2011-01-01
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Stochastic cooling technology at Fermilab
Pasquinelli, R.J. E-mail: pasquin@fnal.gov
2004-10-11
The first antiproton cooling systems were installed and commissioned at Fermilab in 1984-1985. In the interim period, there have been several major upgrades, system improvements, and complete reincarnation of cooling systems. This paper will present some of the technology that was pioneered at Fermilab to implement stochastic cooling systems in both the Antiproton Source and Recycler accelerators. Current performance data will also be presented.
Stochastic analysis of biochemical systems
Anderson, David F
2015-01-01
This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations, and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other ar...
Stochastic gravity: beyond semiclassical gravity
Verdaguer, E [Departament de Fisica Fonamental and CER en Astrofisica, Fisica de Particules i Cosmologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)
2007-05-15
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The semiclassical theory may be obtained from the quantum field theory of gravity interacting with N matter fields in the large N limit. This theory breaks down when the fields quantum fluctuations are important. Stochastic gravity goes beyond the semiclassical limit and allows for a systematic and self-consistent description of the metric fluctuations induced by these quantum fluctuations. The correlation functions of the metric fluctuations obtained in stochastic gravity reproduce the correlation functions in the quantum theory to leading order in an 1/N expansion. Two main applications of stochastic gravity are discussed. The first, in cosmology, to obtain the spectrum of primordial metric perturbations induced by the inflaton fluctuations, even beyond the linear approximation. The second, in black hole physics, to study the fluctuations of the horizon of an evaporating black hole.
Information Anatomy of Stochastic Equilibria
Sarah Marzen
2014-08-01
Full Text Available A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii with a linear drift term (Ornstein–Uhlenbeck, but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.
Nonlinear and Stochastic Morphological Segregation
Blanton, M R
1999-01-01
I perform a joint counts-in-cells analysis of galaxies of different spectral types using the Las Campanas Redshift Survey (LCRS). Using a maximum-likelihood technique to fit for the relationship between the density fields of early- and late-type galaxies, I find a relative linear bias of $b=0.76\\pm 0.02$. This technique can probe the nonlinearity and stochasticity of the relationship as well. However, the degree to which nonlinear and stochastic fits improve upon the linear fit turns out to depend on the redshift range in question. In particular, there seems to be a systematic difference between the high- and low-redshift halves of the data (respectively, further than and closer than $cz\\approx 36,000$ km/s); all of the signal of stochasticity and nonlinearity comes from the low-redshift portion. Analysis of mock catalogs shows that the peculiar geometry and variable flux limits of the LCRS do not cause this effect. I speculate that the central surface brightness selection criteria of the LCRS may be responsi...
Mechanical Autonomous Stochastic Heat Engine
Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara
2016-07-01
Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.
Business Cycles, Financial Crises, and Stock Volatility
G. William Schwert
1989-01-01
This paper shows that stock volatility increases during recessions and financial crises from 1834-1987. The evidence reinforces the notion that stock prices are an important business cycle indicator. Using two different statistical models for stock volatility, I show that volatility increases after major financial crises. Moreover. stock volatility decreases and stock prices rise before the Fed increases margin requirements. Thus, there is little reason to believe that public policies can con...
Decomposing European bond and equity volatility
Christiansen, Charlotte
The paper investigates volatility spillover from US and aggregate European asset markets into European national asset markets. A main contribution is that bond and equity volatilities are analyzed simultaneously. A new model belonging to the "volatilityspillover" family is suggested: The conditio...... (stock) volatilities are mainly influenced by bond (stock) effects. Global, regional, and local volatility effects are all important. The introduction of the euro is associated with a structural break....
Exponential Smoothing, Long Memory and Volatility Prediction
Proietti, Tommaso
Extracting and forecasting the volatility of financial markets is an important empirical problem. The paper provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, and proposes a new predictor that can be seen as extensi...... methods for forecasting realized volatility, and that the estimated model confidence sets include the newly proposed fractional lag predictor in all occurrences....
Possible Sources of Polar Volatiles
Schultz, P. H.
2011-12-01
Extensive analyses of returned Apollo samples demonstrated that the Moon is extremely volatile poor. While this conclusion remains true, various measurements since the late 90's implicated the presence of water: e.g., enhanced reflection of circularly polarized radar signals and suppression of epithermal neutrons near the poles. More recently, traces of H2O have been discovered inside volcanic glass, along with more significant amounts residing in hydrous minerals (apatite) returned from both highland and mare landing sites. Three recent lunar missions (DIXI, M3, Cassini) identified hydrous phases on/near the lunar surface, whereas the LCROSS probe detected significant quantities of volatiles (OH, H2O and other volatiles) excavated by the Centaur impact. These new mission results and sample studies, however, now allow testing different hypotheses for the generation, trapping, and replenishment of these volatiles. Solar-proton implantation must contribute to the hydrous phases in the lunar regolith in order to account for the observed time-varying abundances and occurrence near the lunar equator. This also cannot be the entire story. The relatively low speed LCROSS-Centaur impact (2.5km/s) could not vaporize such hydrous minerals, yet emissions lines of OH (from the thermal disassociation of H2O), along with other compounds (CO2, NH2) were detected within the first second, before ejecta could reach sunlight. Telescopic observations by Potter and Morgan (1985) discovered a tenuous lunar atmosphere of Na, but the LCROSS UV/Vis spectrometer did not detect the Na-D line until after the ejecta reached sunlight (along with a line pair attributed to Ag). With time, other volatile species emerged (OH, CO). The LAMP instrument on the Lunar Reconnaissance Orbiter had a different viewpoint from the side (rather than from above) and detected many other atomic species release by the LCROSS-Centaur impact. Consequently, it appears that there is a stratigraphy for trapped species
Dynamics Model Applied to Pricing Options with Uncertain Volatility
Lorella Fatone
2012-01-01
model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known equispaced discrete time values. Statistical tests were used to estimate the statistical significance of the two parameters of the Black-Scholes model: the volatility and the drift. The effects of these estimates on the option pricing problem were investigated. In particular, the pricing of an option with uncertain volatility in the Black-Scholes framework was revisited, and a statistical significance was associated with the price intervals determined using the Black-Scholes-Barenblatt equations. Numerical experiments involving synthetic and real data were presented. The real data considered were the daily closing values of the S&P500 index and the associated European call and put option prices in the year 2005. The method proposed here for calibrating the Black-Scholes dynamics model could be extended to other science and engineering models that may be expressed in terms of stochastic dynamical systems.
Oil Volatility Risk and Expected Stock Returns
Christoffersen, Peter; Pan, Xuhui (Nick)
After the financialization of commodity futures markets in 2004-05 oil volatility has become a strong predictor of returns and volatility of the overall stock market. Furthermore, stocks' exposure to oil volatility risk now drives the cross-section of expected returns. The difference in average r...
Volatiles in inter-specific bacterial interactions
Tyc, O.; Zweers, H.; De Boer, W.; Garbeva, P.V.
2015-01-01
The importance of volatile organic compounds for functioning of microbes is receiving increased research attention. However, to date very little is known on how inter-specific bacterial interactions effect volatiles production as most studies have been focused on volatiles produced by monocultures o
Volatiles in inter-specific bacterial interactions
Tyc, O.; Zweers, H.; De Boer, W.; Garbeva, P.V.
2015-01-01
The importance of volatile organic compounds for functioning of microbes is receiving increased research attention. However, to date very little is known on how inter-specific bacterial interactions effect volatiles production as most studies have been focused on volatiles produced by monocultures
Ammonia volatilization from intensively managed dairy pastures.
Bussink, D.W.
1996-01-01
The objectives of this thesis are (i) to quantify NH _{3} volatilization from grassland, (ii) to gain understanding of the NH3 volatilization processes on grassland and (iii) to study measures how to reduce NH _{3} volatilization from gra
Oil Volatility Risk and Expected Stock Returns
Christoffersen, Peter; Pan, Xuhui (Nick)
After the financialization of commodity futures markets in 2004-05 oil volatility has become a strong predictor of returns and volatility of the overall stock market. Furthermore, stocks' exposure to oil volatility risk now drives the cross-section of expected returns. The difference in average r...
Cost Linkages Transmit Volatility Across Markets
Nguyen, Daniel Xuyen; Schaur, Georg
to link the domestic and export supply costs. This theoretical contribution has two new implications for the exporting firm. First, the demand volatility in the foreign market now directly affects the firm's domestic sales volatility. Second, firms hedge domestic demand volatility with exports. The model...
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...