Applied Stochastic Control of Jump Diffusions

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Springer Science & Business Media, Mar 30, 2006 - Mathematics - 214 pages
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Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

 

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Contents

Contents
1
Optimal Stopping of Jump Diffusions
27
Stochastic Control of Jump Diffusions 39
38
Combined Optimal Stopping and Stochastic Control
59
Singular Control for Jump Diffusions
71
Impulse Control of Jump Diffusions
81
Approximating Impulse Control of Diffusions
97
Combined Stochastic Control and Impulse Control
113
Viscosity Solutions
123
Solutions of Selected Exercises 149
148
References
197
Index 207
206
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About the author (2006)

Bernt Oksendal is a proven Springer author. His book, Stochastic Differential Equations: An Introduction with Applications, has sold over 10,000 copies and has been translated into Japanese and Chinese.

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