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 Levy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Stochastic Calculus with Jump Diffusions.- Optimal Stopping of Jump Diffusions.- Stochastic Control of Jump Diffusions.- Combined Optimal Stopping and Stochastic Control of Jump Diffusions.- Singular Control for Jump Diffusions.- Impulse Control of Jump Diffusions.- Approximating Impulse Control by Iterated Optimal Stopping.- Combined Stochastic Control and Impulse Control of Jump Diffusions.- Viscosity Solutions.- Optimal Control of Random Jump Fields and Partial Information Control.- Solutions of Selected Exercises.
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- ID: 9783540698258
2nd Revised edition
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