Stochastic Control in Discrete and Continuous Time

1. Front Matter

   Pages 1-9

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2. Stochastic Control over Discrete Time

   • Atle Seierstad

   Pages 1-82

3. The HJB Equation for Deterministic Control

   • Atle Seierstad

   Pages 1-31

4. Piecewise Deterministic Optimal Control Problems

   • Atle Seierstad

   Pages 1-70

5. Control of Diffusions

   • Atle Seierstad

   Pages 1-70

6. Appendix: Probability, Concepts, and Results

   • Atle Seierstad

   Pages 1-22

7. Back Matter

   Pages 1-14

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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.

• Probability theory
• calculus
• optimal control
• optimal stopping problem
• programming
• stochastic dynamic programming

From the reviews:

"This book provides a comprehensive introduction to stochastic control. … The treatment is at the level of a first course, with several examples and exercises. The book can be used by undergraduate students, but also by graduate students, engineers and others who study control, systems and related areas or want to extend their knowledge in these topics." (Krzysztof Szajowski, Mathematical Reviews, Issue 2009 j)

• Dept. Economics, University of Oslo, Oslo, Norway

  Atle Seierstad

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