Download or read book Bias Corrected Least Squares Monte Carlo for Utility Based Optimal Stochastic Control Problems written by Johan Andreasson and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Least-Squares Monte Carlo method has gained popularity recent years due to its ability to handle multi-dimensional stochastic control problems without restrictions on the state dynamics, including problems with state variables affected by control. However, when applied to stochastic control problems in the multiperiod expected utility models, the regression t tends to contain errors which accumulate over time and typically blow up the numerical solution. In this paper we propose to transform the value function of stochastic control problems to improve the regression t, and then using either the 'Smearing Estimate' or 'Controlled Heteroskedasticity' to avoid the re-transformation bias. We also present and utilise recent improvements in Least-Squares Monte Carlo algorithms such as control randomisation with policy iteration to avoid regression errors from accumulating. Presented numerical examples demonstrate that our transformation method allows for control of disturbance terms to be handled correctly and leads to an accurate solution. In addition, in the forward simulation stage of the algorithm, we propose a re-sampling of state variables at each time step instead of simulating continuous paths, to improve the exploration of the state space that also appears to be important to obtain a stable and accurate solution for expected utility models.

Download or read book Mixing Monte Carlo and Partial Differential Equation Methods For Multi dimensional Optimal Stopping Problems Under Stochastic Volatility written by David Farahany and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we develop a numerical approach for solving multi-dimensional optimal stopping problems (OSPs) under stochastic volatility (SV) that combines least squares Monte Carlo (LSMC) with partial differential equation (PDE) techniques. The algorithm provides dimensional reduction from the PDE and regression perspective along with variance and dimensional reduction from the MC perspective. In Chapter 2, we begin by laying the mathematical foundation of mixed MC-PDE techniques for OSPs. Next, we show the basic mechanics of the algorithm and, under certain mild assumptions, prove it converges almost surely. We apply the algorithm to the one dimensional Heston model and demonstrate that the hybrid algorithm outperforms traditional LSMC techniques in terms of both estimating prices and optimal exercise boundaries (OEBs). In Chapter 3 we describe methods for reducing the complexity and run time of the algorithm along with techniques for computing sensitivities. To reduce the complexity, we apply two methods: clustering via sufficient statistics and multi-level Monte Carlo (mlMC)/multi-grids. While the clustering method allows us to reduce computational run times by a third for high dimensional problems, mlMC provides an order of magnitude reduction in complexity. To compute sensitivities, we employ a grid based method for derivatives with respect to the asset, S, and an MC method that uses initial dispersions for sensitivities with respect to variance, v. To test our approximations and computation of sensitivities, we revisit the one-dimensional Heston model and find our approximations introduce little-to-no error and that our computation of sensitivities is highly accurate in comparison to standard LSMC. To demonstrate the utility of our new computational techniques, we apply the hybrid algorithm to the multi-dimensional Heston model and show that the algorithm is highly accurate in terms of estimating prices, OEBs, and sensitivities, especially in comparison to standard LSMC. In Chapter 4 we highlight the importance of multi-factor SV models and apply our hybrid algorithm to two specific examples: the Double Heston model and a mean-reverting commodity model with jumps. Again, we were able to obtain low variance estimates of the prices, OEBs, and sensitivities.

Download or read book Student Solutions Manual to accompany Simulation and the Monte Carlo Method Student Solutions Manual written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2012-01-20 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo Variance reduction techniques such as the transform likelihood ratio method and the screening method The score function method for sensitivity analysis The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization The cross-entropy method to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB® programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

Download or read book Optimization of Weighted Monte Carlo Methods written by Gennadii A. Mikhailov and published by Springer. This book was released on 1992-02-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent statistical experiments to be simulated simultaneously. The weighted Monte Carlo estimates are constructed in order to diminish errors and to obtain dependent estimates for the calculated functionals for different values of parameters of the problem, i.e., to improve the functional dependence. In addition, the weighted estimates make it possible to evaluate special functionals, for example, the derivatives with respect to the parameters. There are many works concerned with the development of the weighted estimates. In Chap. 1 we give the necessary information about these works and present a set of illustrations. The rest of the book is devoted to the solution of a series of mathematical problems related to the optimization of the weighted Monte Carlo estimates.

Download or read book Conditional Monte Carlo written by Michael C. Fu and published by Springer. This book was released on 1997-03-31 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditional Monte Carlo: Gradient Estimation and Optimization Applications deals with various gradient estimation techniques of perturbation analysis based on the use of conditional expectation. The primary setting is discrete-event stochastic simulation. This book presents applications to queueing and inventory, and to other diverse areas such as financial derivatives, pricing and statistical quality control. To researchers already in the area, this book offers a unified perspective and adequately summarizes the state of the art. To researchers new to the area, this book offers a more systematic and accessible means of understanding the techniques without having to scour through the immense literature and learn a new set of notation with each paper. To practitioners, this book provides a number of diverse application areas that makes the intuition accessible without having to fully commit to understanding all the theoretical niceties. In sum, the objectives of this monograph are two-fold: to bring together many of the interesting developments in perturbation analysis based on conditioning under a more unified framework, and to illustrate the diversity of applications to which these techniques can be applied. Conditional Monte Carlo: Gradient Estimation and Optimization Applications is suitable as a secondary text for graduate level courses on stochastic simulations, and as a reference for researchers and practitioners in industry.

Download or read book Least Squares Monte Carlo for Backward Stochastic Differential Equations written by David Stahl and published by . This book was released on 2012 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Regression Based Monte Carlo Methods for Stochastic Control Models written by Yao Tung Huang and published by . This book was released on 2016 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present the regression-based Monte Carlo simulation algorithms for solving the stochastic control models associated with pricing and hedging of the Guaranteed Lifelong Withdrawal Benefit (GLWB) in variable annuities, where the dynamics of the underlying fund value is assumed to evolve according to the stochastic volatility model. The GLWB offers a lifelong withdrawal benefit even when the policy account value becomes zero while the policyholder remains alive. Upon death, the remaining account value will be paid to the beneficiary as a death benefit. The bang-bang control strategy analyzed under the assumption of maximization of the policyholder's expected cash flow reduces the strategy space of optimal withdrawal policies to three choices: zero withdrawal, withdrawal at the contractual amount or complete surrender. The impact on the GLWB value under various withdrawal behaviors of the policyholder is examined. We also analyze the pricing properties of GLWB subject to different model parameter values and structural features.

Download or read book The use of Monte Carlo techniques for the optimization of stochastic control systems written by Chia Choon Wei and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Simulation Based Methods for Optimal Stopping and Control written by Denis Belomestny and published by Palgrave Macmillan. This book was released on 2018-02-04 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an advanced guide to optimal stopping and control, focusing on advanced Monte Carlo simulation and its application to finance. Written for quantitative finance practitioners and researchers in academia, the book looks at the classical simulation based algorithms before introducing some of the new, cutting edge approaches under development.

Download or read book Optimization of Weighted Monte Carlo Methods written by Gennadii A. Mikhailov and published by Springer. This book was released on 1992 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent statistical experiments to be simulated simultaneously. The weighted Monte Carlo estimates are constructed in order to diminish errors and to obtain dependent estimates for the calculated functionals for different values of parameters of the problem, i.e., to improve the functional dependence. In addition, the weighted estimates make it possible to evaluate special functionals, for example, the derivatives with respect to the parameters. There are many works concerned with the development of the weighted estimates. In Chap. 1 we give the necessary information about these works and present a set of illustrations. The rest of the book is devoted to the solution of a series of mathematical problems related to the optimization of the weighted Monte Carlo estimates.

Download or read book Regression based Monte Carlo Methods with Optimal Control Variates written by Stefan Häfner and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Application of Monte Carlo Method to Optimal Control Problems written by Hiromitsu Kumamoto and published by . This book was released on 1972 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Correcting the Monte Carlo Optimal stopping Bias written by Tyson L. Whitehead and published by . This book was released on 2008 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Technometrics written by and published by . This book was released on 2004 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of Stochastic Optimal Control to Economics and Finance written by Salvatore Federico and published by . This book was released on 2020-06-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a world dominated by uncertainty, modeling and understanding the optimal behavior of agents is of the utmost importance. Many problems in economics, finance, and actuarial science naturally require decision makers to undertake choices in stochastic environments. Examples include optimal individual consumption and retirement choices, optimal management of portfolios and risk, hedging, optimal timing issues in pricing American options, and investment decisions. Stochastic control theory provides the methods and results to tackle all such problems. This book is a collection of the papers published in the Special Issue "Applications of Stochastic Optimal Control to Economics and Finance", which appeared in the open access journal Risks in 2019. It contains seven peer-reviewed papers dealing with stochastic control models motivated by important questions in economics and finance. Each model is rigorously mathematically funded and treated, and the numerical methods are employed to derive the optimal solution. The topics of the book's chapters range from optimal public debt management to optimal reinsurance, real options in energy markets, and optimal portfolio choice in partial and complete information settings. From a mathematical point of view, techniques and arguments of dynamic programming theory, filtering theory, optimal stopping, one-dimensional diffusions and multi-dimensional jump processes are used.

Download or read book Reinforcement Learning second edition written by Richard S. Sutton and published by MIT Press. This book was released on 2018-11-13 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.

Download or read book Current Index to Statistics Applications Methods and Theory written by and published by . This book was released on 1994 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.