Stochastic Control in Discrete and Continuous Time

This book is a comprehensive introduction to stochastic control problems in both discrete and continuous time. It covers stochastic dynamic programming and the optimal stopping problem for discrete time with a finite or infinite horizon.

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.

Offers broad coverage of three types of stochastic control problems at an elementary level Includes numerous illustrative examples and exercises Can be used in a classroom setting or for self-study

Inhalt
Stochastic Control over Discrete Time.- The HJB Equation for Deterministic Control.- Piecewise Deterministic Optimal Control Problems.- Control of Diffusions.- Appendix: Probability, Concepts, and Results.