Mou-Hsiung Chang (eds.)9780387758053, 0387758054, 038775816X
This research monograph develops the Hamilton-Jacobi-Bellman (HJB) theory through dynamic programming principle for a class of optimal control problems for stochastic hereditary differential systems. It is driven by a standard Brownian motion and with a bounded memory or an infinite but fading memory.
The optimal control problems treated in this book include optimal classical control and optimal stopping with a bounded memory and over finite time horizon.
This book can be used as an introduction for researchers and graduate students who have a special interest in learning and entering the research areas in stochastic control theory with memories. Each chapter contains a summary.
Mou-Hsiung Chang is a program manager at the Division of Mathematical Sciences for the U.S. Army Research Office.
Table of contents :
Front Matter….Pages I-XVIII
Introduction and Summary….Pages 1-36
Stochastic Hereditary Differential Equations….Pages 37-78
Stochastic Calculus….Pages 79-125
Optimal Classical Control….Pages 127-201
Optimal Stopping….Pages 203-244
Discrete Approximations….Pages 245-292
Option Pricing….Pages 293-331
Hereditary Portfolio Optimization….Pages 333-391
Back Matter….Pages 393-406
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