Applied Stochastic Control of Jump Diffusions

✍ Scribed by Bernt Øksendal, Agnès Sulem

• Year: 2007
• Tongue: English
• Leaves: 215
• Edition: 2nd
• Category: Library

✦ Synopsis

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 L?vy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

✦ Table of Contents

Cover......Page 1
Applied Stochastic
Control
of Jump Diffusions......Page 3
ISBN 3540140239......Page 4
Preface......Page 6
Contents......Page 8
1
Stochastic Calculus with Jump diffusions......Page 10
2
Optimal Stopping of Jump Diffusions......Page 35
3
Stochastic Control of Jump Diffusions......Page 46
4
Combined Optimal Stopping
and Stochastic Control of Jump Diffusions......Page 66
5
Singular Control for Jump Diffusions......Page 78
6
Impulse Control of Jump Diffusions......Page 88
7
Approximating Impulse Control of Diffusions
by Iterated Optimal Stopping......Page 103
8
Combined Stochastic Control
and Impulse Control of Jump Diffusions......Page 119
9
Viscosity Solutions......Page 129
10
Solutions of Selected Exercises......Page 154
References......Page 202
Notation and Symbols......Page 207
Index......Page 210