Stochastic Control

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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 : 51,8 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.

Stochastic Control Theory

Makiko Nisio
Stochastic Control Theory Book PDF

Author : Makiko Nisio
Publisher : Springer
Page : 263 pages
File Size : 41,5 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 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 : 43,7 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.​

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 : 46,7 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.

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 : 42,9 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.

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 : 50,5 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 Control in Insurance

Hanspeter Schmidli
Stochastic Control in Insurance Book PDF

Author : Hanspeter Schmidli
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 47,5 Mb
Release : 2007-11-20
Category : Business & Economics
ISBN : 9781848000032

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Stochastic Control in Insurance by Hanspeter Schmidli Pdf

Yet again, here is a Springer volume that offers readers something completely new. Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals. Not any more: this is the first book to systematically present these methods in one volume. The author starts with a short introduction to stochastic control techniques, then applies the principles to several problems. These examples show how verification theorems and existence theorems may be proved, and that the non-diffusion case is simpler than the diffusion case. Schmidli’s brilliant text also includes a number of appendices, a vital resource for those in both academic and professional settings.

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 : 44,5 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 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 : 42,9 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.

Linear Stochastic Control Systems

Goong Chen,Guanrong Chen,Shih-Hsun Hsu
Linear Stochastic Control Systems Book PDF

Author : Goong Chen,Guanrong Chen,Shih-Hsun Hsu
Publisher : CRC Press
Page : 404 pages
File Size : 44,6 Mb
Release : 1995-07-12
Category : Business & Economics
ISBN : 0849380758

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Linear Stochastic Control Systems by Goong Chen,Guanrong Chen,Shih-Hsun Hsu Pdf

Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.

Applied Stochastic Control of Jump Diffusions

Bernt Øksendal,Agnès Sulem
Applied Stochastic Control of Jump Diffusions Book PDF

Author : Bernt Øksendal,Agnès Sulem
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 47,6 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9783540698265

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Applied Stochastic Control of Jump Diffusions by Bernt Øksendal,Agnès Sulem Pdf

Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

Stochastic Multi-Stage Optimization

Pierre Carpentier,Jean-Philippe Chancelier,Guy Cohen,Michel De Lara
Stochastic Multi Stage Optimization Book PDF

Author : Pierre Carpentier,Jean-Philippe Chancelier,Guy Cohen,Michel De Lara
Publisher : Springer
Page : 362 pages
File Size : 42,7 Mb
Release : 2015-05-05
Category : Mathematics
ISBN : 9783319181387

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Stochastic Multi-Stage Optimization by Pierre Carpentier,Jean-Philippe Chancelier,Guy Cohen,Michel De Lara Pdf

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.

Modeling, Stochastic Control, Optimization, and Applications

George Yin,Qing Zhang
Modeling Stochastic Control Optimization and Applications Book PDF

Author : George Yin,Qing Zhang
Publisher : Springer
Page : 599 pages
File Size : 52,8 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9783030254988

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Modeling, Stochastic Control, Optimization, and Applications by George Yin,Qing Zhang Pdf

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Rational Matrix Equations in Stochastic Control

Tobias Damm
Rational Matrix Equations in Stochastic Control Book PDF

Author : Tobias Damm
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 51,9 Mb
Release : 2004-01-23
Category : Mathematics
ISBN : 3540205160

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Rational Matrix Equations in Stochastic Control by Tobias Damm Pdf

This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.

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 : 52,7 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.