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 Numerical Solutions to Stochastic Control Problems written by Zhiyi Shen and published by . This book was released on 2019 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this thesis is to develop theoretically sound as well as numerically efficient Least Squares Monte Carlo (LSMC) methods for solving discrete-time stochastic control problems motivated by insurance and finance problems. Despite its popularity in solving optimal stopping problems, the application of the LSMC method to stochastic control problems is hampered by several challenges. Firstly, the simulation of the state process is intricate in the absence of the optimal control policy in prior. Secondly, numerical methods only warrant the approximation accuracy of the value function over a bounded domain, which is incompatible with the unbounded set the state variable dwells in. Thirdly, given a considerable number of simulated paths, regression methods are computationally challenging. This thesis responds to the above problems. Chapter 2 develops a novel LSMC algorithm to solve discrete-time stochastic optimal control problems, referred to as the Backward Simulation and Backward Updating (BSBU) algorithm. The BSBU algorithm has three pillars: a construction of auxiliary stochastic control model, an artificial simulation of the post-action value of state process, and a shape-preserving sieve estimation method which equip the algorithm with a number of merits including obviating forward simulation and control randomization, evading extrapolating the value function, and alleviating computational burden of the tuning parameter selection. Chapter 3 proposes an alternative LSMC algorithm which directly approximates the optimal value function at each time step instead of the continuation function. This brings the benefits of faster convergence rate and closed-form expressions of the value function compared with the previously developed BSBU algorithm. We also develop a general argument for constructing an auxiliary stochastic control problem which inherits the continuity, monotonicity, and concavity of the original problem. This argument renders the LSMC algorithm circumvent extrapolating the value function in the backward recursion and can well adapt to other numerical methods. Chapter 4 studies a complicated stochastic control problem: the no-arbitrage pricing of the "Polaris Choice IV" variable annuities issued by the American International Group. The Polaris allows the income base to lock in the high-water-mark of the investment account over a certain monitoring period which is related to the timing of the policyholder's first withdrawal. By prudently introducing certain auxiliary state and control variables, we formulate the pricing problem into a Markovian stochastic optimal control framework. With a slight modification on the fee structure, we prove the existence of a bang-bang solution to the stochastic control problem: the policyholder's optimal withdrawal strategy is limited to a few choices. Accordingly, the price of the modified contract can be solved by the BSBU algorithm. Finally, we prove that the price of the modified contract is an upper bound for that of the Polaris with the real fee structure. Numerical experiments show that this bound is fairly tight.
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 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 Regression Methods for Stochastic Control Problems written by Denis Belomestny and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea of the algorithms is to simulate a set of trajectories under some reference measure and to use a dynamic program formulation combined with fast methods for approximating conditional expectations and functional optimizations on these trajectories. Theoretical properties of the presented algorithms are investigated and convergence to the optimal solution is proved under mild assumptions. Finally, we present numerical results showing the efficiency of regression algorithms in a case of a high-dimensional Bermudan basket options, in a model with a large investor and transaction costs.
Download or read book Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Download or read book Monte Carlo Simulation Based Statistical Modeling written by Ding-Geng (Din) Chen and published by Springer. This book was released on 2017-02-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.
Download or read book Monte Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2008-10-20 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Download or read book Monte Carlo Methods written by J. Hammersley and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Download or read book Monte Carlo Methods for Stochastic Differential Equations and Their Applications written by Andrew Bradford Leach and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce computationally efficient Monte Carlo methods for studying the statistics of stochastic differential equations in two distinct settings. In the first, we derive importance sampling methods for data assimilation when the noise in the model and observations are small. The methods are formulated in discrete time, where the "posterior" distribution we want to sample from can be analyzed in an accessible small noise expansion. We show that a "symmetrization" procedure akin to antithetic coupling can improve the order of accuracy of the sampling methods, which is illustrated with numerical examples. In the second setting, we develop "stochastic continuation" methods to estimate level sets for statistics of stochastic differential equations with respect to their parameters. We adapt Keller's Pseudo-Arclength continuation method to this setting using stochastic approximation, and generalized least squares regression. Furthermore, we show that the methods can be improved through the use of coupling methods to reduce the variance of the derivative estimates that are involved.
Download or read book Monte Carlo Methods written by Adrian Barbu and published by Springer Nature. This book was released on 2020-02-24 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 331 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 Handbook in Monte Carlo Simulation written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2014-06-20 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation.
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.
