Introduction To Stochastic Control Theory

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Introduction to Stochastic Control Theory

Karl J. Åström
Introduction to Stochastic Control Theory Book PDF

Author : Karl J. Åström
Publisher : Courier Corporation
Page : 322 pages
File Size : 53,9 Mb
Release : 2012-05-11
Category : Technology & Engineering
ISBN : 9780486138275

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Introduction to Stochastic Control Theory by Karl J. Åström Pdf

This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria, it covers discrete time as well as continuous time systems. The first three chapters provide motivation and background material on stochastic processes, followed by an analysis of dynamical systems with inputs of stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed, along with an example of an industrial application of this theory. Subsequent discussions cover filtering and prediction theory as well as the general stochastic control problem for linear systems with quadratic criteria. Each chapter begins with the discrete time version of a problem and progresses to a more challenging continuous time version of the same problem. Prerequisites include courses in analysis and probability theory in addition to a course in dynamical systems that covers frequency response and the state-space approach for continuous time and discrete time systems.

Stochastic Control Theory

Makiko Nisio
Stochastic Control Theory Book PDF

Author : Makiko Nisio
Publisher : Springer
Page : 263 pages
File Size : 40,9 Mb
Release : 2014-11-27
Category : Mathematics
ISBN : 9784431551232

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Stochastic Control Theory by Makiko Nisio Pdf

This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

Optimal Estimation

Frank L. Lewis
Optimal Estimation Book PDF

Author : Frank L. Lewis
Publisher : Wiley-Interscience
Page : 408 pages
File Size : 43,6 Mb
Release : 1986-04-15
Category : Mathematics
ISBN : UOM:39015009833727

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Optimal Estimation by Frank L. Lewis Pdf

Describes the use of optimal control and estimation in the design of robots, controlled mechanisms, and navigation and guidance systems. Covers control theory specifically for students with minimal background in probability theory. Presents optimal estimation theory as a tutorial with a direct, well-organized approach and a parallel treatment of discrete and continuous time systems. Gives practical examples and computer simulations. Provides enough mathematical rigor to put results on a firm foundation without an overwhelming amount of proofs and theorems.

Stochastic Control in Discrete and Continuous Time

Atle Seierstad
Stochastic Control in Discrete and Continuous Time Book PDF

Author : Atle Seierstad
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 48,9 Mb
Release : 2010-07-03
Category : Mathematics
ISBN : 9780387766171

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Stochastic Control in Discrete and Continuous Time by Atle Seierstad Pdf

This book contains an introduction to three topics in stochastic control: discrete time stochastic control, i. e. , stochastic dynamic programming (Chapter 1), piecewise - terministic control problems (Chapter 3), and control of Ito diffusions (Chapter 4). The chapters include treatments of optimal stopping problems. An Appendix - calls material from elementary probability theory and gives heuristic explanations of certain more advanced tools in probability theory. The book will hopefully be of interest to students in several ?elds: economics, engineering, operations research, ?nance, business, mathematics. In economics and business administration, graduate students should readily be able to read it, and the mathematical level can be suitable for advanced undergraduates in mathem- ics and science. The prerequisites for reading the book are only a calculus course and a course in elementary probability. (Certain technical comments may demand a slightly better background. ) As this book perhaps (and hopefully) will be read by readers with widely diff- ing backgrounds, some general advice may be useful: Don’t be put off if paragraphs, comments, or remarks contain material of a seemingly more technical nature that you don’t understand. Just skip such material and continue reading, it will surely not be needed in order to understand the main ideas and results. The presentation avoids the use of measure theory.

Optimal and Robust Estimation

Frank L. Lewis,Lihua Xie,Dan Popa
Optimal and Robust Estimation Book PDF

Author : Frank L. Lewis,Lihua Xie,Dan Popa
Publisher : CRC Press
Page : 546 pages
File Size : 41,7 Mb
Release : 2017-12-19
Category : Technology & Engineering
ISBN : 9781420008296

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Optimal and Robust Estimation by Frank L. Lewis,Lihua Xie,Dan Popa Pdf

More than a decade ago, world-renowned control systems authority Frank L. Lewis introduced what would become a standard textbook on estimation, under the title Optimal Estimation, used in top universities throughout the world. The time has come for a new edition of this classic text, and Lewis enlisted the aid of two accomplished experts to bring the book completely up to date with the estimation methods driving today's high-performance systems. A Classic Revisited Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition reflects new developments in estimation theory and design techniques. As the title suggests, the major feature of this edition is the inclusion of robust methods. Three new chapters cover the robust Kalman filter, H-infinity filtering, and H-infinity filtering of discrete-time systems. Modern Tools for Tomorrow's Engineers This text overflows with examples that highlight practical applications of the theory and concepts. Design algorithms appear conveniently in tables, allowing students quick reference, easy implementation into software, and intuitive comparisons for selecting the best algorithm for a given application. In addition, downloadable MATLAB® code allows students to gain hands-on experience with industry-standard software tools for a wide variety of applications. This cutting-edge and highly interactive text makes teaching, and learning, estimation methods easier and more modern than ever.

Stochastic Optimal Control in Infinite Dimension

Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Stochastic Optimal Control in Infinite Dimension Book PDF

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 49,7 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.

Deterministic and Stochastic Optimal Control

Wendell H. Fleming,Raymond W. Rishel
Deterministic and Stochastic Optimal Control Book PDF

Author : Wendell H. Fleming,Raymond W. Rishel
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263807

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Deterministic and Stochastic Optimal Control by Wendell H. Fleming,Raymond W. Rishel Pdf

This book may be regarded as consisting of two parts. In Chapters I-IV we pre sent what we regard as essential topics in an introduction to deterministic optimal control theory. This material has been used by the authors for one semester graduate-level courses at Brown University and the University of Kentucky. The simplest problem in calculus of variations is taken as the point of departure, in Chapter I. Chapters II, III, and IV deal with necessary conditions for an opti mum, existence and regularity theorems for optimal controls, and the method of dynamic programming. The beginning reader may find it useful first to learn the main results, corollaries, and examples. These tend to be found in the earlier parts of each chapter. We have deliberately postponed some difficult technical proofs to later parts of these chapters. In the second part of the book we give an introduction to stochastic optimal control for Markov diffusion processes. Our treatment follows the dynamic pro gramming method, and depends on the intimate relationship between second order partial differential equations of parabolic type and stochastic differential equations. This relationship is reviewed in Chapter V, which may be read inde pendently of Chapters I-IV. Chapter VI is based to a considerable extent on the authors' work in stochastic control since 1961. It also includes two other topics important for applications, namely, the solution to the stochastic linear regulator and the separation principle.

Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions

Jingrui Sun,Jiongmin Yong
Stochastic Linear Quadratic Optimal Control Theory Open Loop and Closed Loop Solutions Book PDF

Author : Jingrui Sun,Jiongmin Yong
Publisher : Springer Nature
Page : 129 pages
File Size : 47,8 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9783030209223

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Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun,Jiongmin Yong Pdf

This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.

Controlled Markov Processes and Viscosity Solutions

Wendell H. Fleming,Halil Mete Soner
Controlled Markov Processes and Viscosity Solutions Book PDF

Author : Wendell H. Fleming,Halil Mete Soner
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 44,7 Mb
Release : 2006-02-04
Category : Mathematics
ISBN : 9780387310718

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Controlled Markov Processes and Viscosity Solutions by Wendell H. Fleming,Halil Mete Soner Pdf

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

Introduction to Stochastic Control

Harold Joseph Kushner
Introduction to Stochastic Control Book PDF

Author : Harold Joseph Kushner
Publisher : Unknown
Page : 414 pages
File Size : 42,6 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015040423660

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Introduction to Stochastic Control by Harold Joseph Kushner Pdf

The text treats stochastic control problems for Markov chains, discrete time Markov processes, and diffusion models, and discusses method of putting other problems into the Markovian framework. Computational methods are discussed and compared for Markov chain problems. Other topics include the fixed and free time of control, discounted cost, minimizing the average cost per unit time, and optimal stopping. Filtering and conrol for linear systems, and stochastic stability for discrete time problems are discussed thoroughly. The book gives a detailed treatment of the simpler problems, and fills the need to introduce the student to the more sophisticated mathematical concepts required for advanced theory by describing their roles and necessity in an intuitive and natural way. Diffusion models are developed as limits of stochastic difference equations and also via the stochastic integral approach. Examples and exercises are included. (Author).

Optimal Control and Estimation

Robert F. Stengel
Optimal Control and Estimation Book PDF

Author : Robert F. Stengel
Publisher : Courier Corporation
Page : 672 pages
File Size : 41,5 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9780486134819

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Optimal Control and Estimation by Robert F. Stengel Pdf

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

Nizar Touzi
Optimal Stochastic Control Stochastic Target Problems and Backward SDE Book PDF

Author : Nizar Touzi
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 41,8 Mb
Release : 2012-09-25
Category : Mathematics
ISBN : 9781461442868

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Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE by Nizar Touzi Pdf

This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.​

Continuous-time Stochastic Control and Optimization with Financial Applications

Huyên Pham
Continuous time Stochastic Control and Optimization with Financial Applications Book PDF

Author : Huyên Pham
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 42,8 Mb
Release : 2009-05-28
Category : Mathematics
ISBN : 9783540895008

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Continuous-time Stochastic Control and Optimization with Financial Applications by Huyên Pham Pdf

Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Numerical Methods for Stochastic Control Problems in Continuous Time

Harold Kushner,Paul G. Dupuis
Numerical Methods for Stochastic Control Problems in Continuous Time Book PDF

Author : Harold Kushner,Paul G. Dupuis
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 51,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461300076

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Numerical Methods for Stochastic Control Problems in Continuous Time by Harold Kushner,Paul G. Dupuis Pdf

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Stochastic Controls

Jiongmin Yong,Xun Yu Zhou
Stochastic Controls Book PDF

Author : Jiongmin Yong,Xun Yu Zhou
Publisher : Springer Science & Business Media
Page : 459 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461214663

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Stochastic Controls by Jiongmin Yong,Xun Yu Zhou Pdf

As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.