Time Inconsistent Control Theory With Finance Applications

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Time-Inconsistent Control Theory with Finance Applications

Author : Tomas Björk
Publisher : Springer Nature
ISBN 13 : 3030818438
Total Pages : 328 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Time-Inconsistent Control Theory with Finance Applications by : Tomas Björk

Download or read book Time-Inconsistent Control Theory with Finance Applications written by Tomas Björk and published by Springer Nature. This book was released on 2021-11-02 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

Time-Inconsistent Control Theory with Finance Applications

Author : Tomas Björk
Publisher :
ISBN 13 : 9783030818449
Total Pages : 0 pages
Book Rating : 4.8/5 (184 download)

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Book Synopsis Time-Inconsistent Control Theory with Finance Applications by : Tomas Björk

Download or read book Time-Inconsistent Control Theory with Finance Applications written by Tomas Björk and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker's preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent's current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

Continuous-time Stochastic Control and Optimization with Financial Applications

Author : Huyên Pham
Publisher : Springer Science & Business Media
ISBN 13 : 3540895000
Total Pages : 243 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham

Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arbitrage Theory in Continuous Time

Author : Tomas Björk
Publisher : OUP Oxford
ISBN 13 : 0191610291
Total Pages : 600 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Björk

Download or read book Arbitrage Theory in Continuous Time written by Tomas Björk and published by OUP Oxford. This book was released on 2009-08-06 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

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

Author : Jingrui Sun
Publisher : Springer Nature
ISBN 13 : 3030209229
Total Pages : 129 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by : Jingrui Sun

Download or read book Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions written by Jingrui Sun and published by Springer Nature. This book was released on 2020-06-29 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Point Processes and Jump Diffusions

Author : Tomas Björk
Publisher : Cambridge University Press
ISBN 13 : 1316518671
Total Pages : 323 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Point Processes and Jump Diffusions by : Tomas Björk

Download or read book Point Processes and Jump Diffusions written by Tomas Björk and published by Cambridge University Press. This book was released on 2021-06-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.

Point Processes and Jump Diffusions

Author : Tomas Björk
Publisher : Cambridge University Press
ISBN 13 : 1009008447
Total Pages : 324 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Point Processes and Jump Diffusions by : Tomas Björk

Download or read book Point Processes and Jump Diffusions written by Tomas Björk and published by Cambridge University Press. This book was released on 2021-06-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of marked point processes on the real line is of great and increasing importance in areas such as insurance mathematics, queuing theory and financial economics. However, the theory is often viewed as technically and conceptually difficult and has proved to be a block for PhD students looking to enter the area. This book gives an intuitive picture of the central concepts as well as the deeper results, while presenting the mathematical theory in a rigorous fashion and discussing applications in filtering theory and financial economics. Consequently, readers will get a deep understanding of the theory and how to use it. A number of exercises of differing levels of difficulty are included, providing opportunities to put new ideas into practice. Graduate students in mathematics, finance and economics will gain a good working knowledge of point-process theory, allowing them to progress to independent research.

Robustness

Author : Lars Peter Hansen
Publisher : Princeton University Press
ISBN 13 : 0691170975
Total Pages : 453 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Robustness by : Lars Peter Hansen

Download or read book Robustness written by Lars Peter Hansen and published by Princeton University Press. This book was released on 2016-06-28 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted? Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics. Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.

Arbitrage Theory in Continuous Time

Author : Tomas Bjork
Publisher : Oxford University Press, USA
ISBN 13 : 0198851618
Total Pages : 584 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Bjork

Download or read book Arbitrage Theory in Continuous Time written by Tomas Bjork and published by Oxford University Press, USA. This book was released on 2020-01-16 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Bjork has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so that these approaches can be studied independently of each other, thus providing the less mathematically-oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.

Stochastic Analysis, Filtering, and Stochastic Optimization

Author : George Yin
Publisher : Springer Nature
ISBN 13 : 3030985199
Total Pages : 466 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Stochastic Analysis, Filtering, and Stochastic Optimization by : George Yin

Download or read book Stochastic Analysis, Filtering, and Stochastic Optimization written by George Yin and published by Springer Nature. This book was released on 2022-04-22 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.

Dynamic Optimization, Second Edition

Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien

Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Introduction to Econophysics

Author : Rosario N. Mantegna
Publisher : Cambridge University Press
ISBN 13 : 1139431226
Total Pages : 164 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Introduction to Econophysics by : Rosario N. Mantegna

Download or read book Introduction to Econophysics written by Rosario N. Mantegna and published by Cambridge University Press. This book was released on 1999-11-13 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Recent Advances in Financial Engineering 2012

Author : Akihiko Takahashi
Publisher : World Scientific
ISBN 13 : 9814571652
Total Pages : 208 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Recent Advances in Financial Engineering 2012 by : Akihiko Takahashi

Download or read book Recent Advances in Financial Engineering 2012 written by Akihiko Takahashi and published by World Scientific. This book was released on 2014-02-24 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Financial Engineering 2012 is the Proceedings of the International Workshop on Finance 2012, which was held at the University of Tokyo on October 30 and 31, 2012. This workshop was organized by the Center for Advanced Research in Finance (CARF), Graduate School of Economics, the University of Tokyo, and Graduate School of Social Sciences, Tokyo Metropolitan University (TMU). This annual workshop, which was first held in 2011, is a successor to the Daiwa International Workshop (2004 to 2008) and the KIER–TMU International Workshop (2009 to 2010). The workshop was designed for the exchange of new ideas in financial engineering and to serves as a bridge between academic researchers and practitioners. To these ends, the speakers shared various interesting ideas, information on new methods, and their up-to-date research results. In the 2012 workshop, we invited nine leading scholars, including three keynote speakers, from various countries, and the two-day workshop resulted in many fruitful discussions. The book consists of eight papers, all refereed, that were related to the presentations at the International Workshop on Finance 2012. In these papers, the latest concepts, methods, and techniques related to current topics in financial engineering are proposed and reviewed. Contents:Forward Prices in Markets Driven by Continuous-Time Autoregressive Processes (F E Benth & S A S Blanco)A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective (T R Bielecki, A Cousin, S Crépey, A Herbertsson)A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part II: Common-Shock Interpretation, Calibration and Hedging Issues (T R Bielecki, A Cousin, S Crépey, A Herbertsson)On the Limit Behavior of Option Hedging Sets Under Transaction Costs (J Grépat)Optimal Execution for Uncertain Market Impact: Derivation and Characterization of a Continuous-Time Value Function (K Ishitani and T Kato)Optimal Investment Timing and Volume Decisions Under Debt Borrowing Constraints (T Shibata and M Nishihara)Fractional Brownian Motions in Financial Models and Their Monte Carlo Simulation (C M Tam)Mean-Variance Pre-Commitment Policies Revisited Via a Mean-Field Technique (A Bensoussan, K C Wong, S C P Yam) Readership: Graduate and postgraduate students of financial engineering and mathematical finance; academics and practitioners; quantitative researchers on financial markets. Keywords:Financial Engineering;Mathematical Finance;Money & Banking;Risk Management;Real Option;Corporate Finance;Computational Finance

Misbehaving: The Making of Behavioral Economics

Author : Richard H. Thaler
Publisher : W. W. Norton & Company
ISBN 13 : 0393246779
Total Pages : 502 pages
Book Rating : 4.3/5 (932 download)

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Book Synopsis Misbehaving: The Making of Behavioral Economics by : Richard H. Thaler

Download or read book Misbehaving: The Making of Behavioral Economics written by Richard H. Thaler and published by W. W. Norton & Company. This book was released on 2015-05-11 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the Nobel Prize in Economics Get ready to change the way you think about economics. Nobel laureate Richard H. Thaler has spent his career studying the radical notion that the central agents in the economy are humans—predictable, error-prone individuals. Misbehaving is his arresting, frequently hilarious account of the struggle to bring an academic discipline back down to earth—and change the way we think about economics, ourselves, and our world. Traditional economics assumes rational actors. Early in his research, Thaler realized these Spock-like automatons were nothing like real people. Whether buying a clock radio, selling basketball tickets, or applying for a mortgage, we all succumb to biases and make decisions that deviate from the standards of rationality assumed by economists. In other words, we misbehave. More importantly, our misbehavior has serious consequences. Dismissed at first by economists as an amusing sideshow, the study of human miscalculations and their effects on markets now drives efforts to make better decisions in our lives, our businesses, and our governments. Coupling recent discoveries in human psychology with a practical understanding of incentives and market behavior, Thaler enlightens readers about how to make smarter decisions in an increasingly mystifying world. He reveals how behavioral economic analysis opens up new ways to look at everything from household finance to assigning faculty offices in a new building, to TV game shows, the NFL draft, and businesses like Uber. Laced with antic stories of Thaler’s spirited battles with the bastions of traditional economic thinking, Misbehaving is a singular look into profound human foibles. When economics meets psychology, the implications for individuals, managers, and policy makers are both profound and entertaining. Shortlisted for the Financial Times & McKinsey Business Book of the Year Award

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

Author : Jingrui Sun
Publisher : Springer Nature
ISBN 13 : 3030483061
Total Pages : 138 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems by : Jingrui Sun

Download or read book Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems written by Jingrui Sun and published by Springer Nature. This book was released on 2020-06-29 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. 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.

Stochastic Controls

Author : Jiongmin Yong
Publisher : Springer Science & Business Media
ISBN 13 : 1461214661
Total Pages : 459 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Controls by : Jiongmin Yong

Download or read book Stochastic Controls written by Jiongmin Yong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.