Overview

The maximum principle and dynamic programming are the two most commonly used approaches in solving optimal control problems. These approaches have been developed independently. The theme of this book is to unify these two approaches, and to demonstrate that the viscosity solution theory provides the framework to unify them.

Full Product Details

Author:   Jiongmin Yong ,  Xun Yu Zhou
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1999 ed.
Volume:   43
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   1.820kg
ISBN:  

9780387987231

ISBN 10:   0387987231
Pages:   439
Publication Date:   22 June 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Basic Stochastic Calculus.- 1. Probability.- 2. Stochastic Processes.- 3. Stopping Times.- 4. Martingales.- 5. Itô’s Integral.- 6. Stochastic Differential Equations.- 2. Stochastic Optimal Control Problems.- 1. Introduction.- 2. Deterministic Cases Revisited.- 3. Examples of Stochastic Control Problems.- 4. Formulations of Stochastic Optimal Control Problems.- 5. Existence of Optimal Controls.- 6. Reachable Sets of Stochastic Control Systems.- 7. Other Stochastic Control Models.- 8. Historical Remarks.- 3. Maximum Principle and Stochastic Hamiltonian Systems.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. Statement of the Stochastic Maximum Principle.- 4. A Proof of the Maximum Principle.- 5. Sufficient Conditions of Optimality.- 6. Problems with State Constraints.- 7. Historical Remarks.- 4. Dynamic Programming and HJB Equations.- 1. Introduction.- 2. The Deterministic Case Revisited.- 3. The Stochastic Principle of Optimality and the HJB Equation.- 4. Other Propertiesof the Value Function.- 5. Viscosity Solutions.- 6. Uniqueness of Viscosity Solutions.- 7. Historical Remarks.- 5. The Relationship Between the Maximum Principle and Dynamic Programming.- 1. Introduction.- 2. Classical Hamilton-Jacobi Theory.- 3. Relationship for Deterministic Systems.- 4. Relationship for Stochastic Systems.- 5. Stochastic Verification Theorems.- 6. Optimal Feedback Controls.- 7. Historical Remarks.- 6. Linear Quadratic Optimal Control Problems.- 1. Introduction.- 2. The Deterministic LQ Problems Revisited.- 3. Formulation of Stochastic LQ Problems.- 4. Finiteness and Solvability.- 5. A Necessary Condition and a Hamiltonian System.- 6. Stochastic Riccati Equations.- 7. Global Solvability of Stochastic Riccati Equations.- 8. A Mean-variance Portfolio Selection Problem.- 9. Historical Remarks.- 7. Backward Stochastic Differential Equations.- 1. Introduction.- 2. Linear Backward Stochastic Differential Equations.- 3. Nonlinear Backward Stochastic Differential Equations.- 4. Feynman—Kac-Type Formulae.- 5. Forward—Backward Stochastic Differential Equations.- 6. Option Pricing Problems.- 7. Historical Remarks.- References.

Reviews

From the reviews: <p>SIAM REVIEW <p> The presentation of this book is systematic and self-containeda ]Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) coursea ]This book is highly recommended to anyone who wishes to study the relationship between Pontryagina (TM)s maximum principle and Bellmana (TM)s dynamic programming principle applied to diffusion processes. <p>MATHEMATICS REVIEW <p>This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. Review

From the reviews: SIAM REVIEW The presentation of this book is systematic and self-contained!Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course!This book is highly recommended to anyone who wishes to study the relationship between Pontryagin's maximum principle and Bellman's dynamic programming principle applied to diffusion processes. MATHEMATICS REVIEW This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. Review

From the reviews: SIAM REVIEW ""The presentation of this book is systematic and self-contained!Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course!This book is highly recommended to anyone who wishes to study the relationship between Pontryagin's maximum principle and Bellman's dynamic programming principle applied to diffusion processes."" MATHEMATICS REVIEW This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. Review

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