Applied Stochastic Control of Jump Diffusions
Description
This book offers 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 extends to both the dynamic programming method and the maximum principle method, as well as the relation between them. The authors formulate the corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities. The text emphasises real-world applications, primarily in the field of finance. All the main results are illustrated by examples, and exercises appear at the end of each chapter with complete solutions, to help the reader understand the theory and learn how to apply it. The 2nd edition adds a new chapter on optimal control of stochastic partial differential equations driven by Lévy processes, along with a new section on optimal stopping with delayed information. Some basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Reviews / Votes
From the reviews:
"The main purpose of this excellent monograph is to give a rigorous non-technical introduction to the most important and useful solution methods of various types of optimal stochastic control problems for jump diffusions and their applications. . All the main results are illustrated by examples and exercises . . This really helps the reader to understand the theory and to see how it can be applied. . This book is a very useful text for students, researchers, and practitioners working in stochastic analysis . ." (Pavel Gapeev, Zentralblatt MATH, Vol. 1074, 2005)
"The focus is on the applied aspect of the theory of control diffusion processes with jumps, particularly in finance and economy. . A relatively large number of examples and exercises (with solutions) is provided, mainly typical models in finance, but also examples in biology, physics, or engineering. . Summing up, this book is a very good addition to the stochastic control literature . ." (Jose-Luis Menaldi, SIAM Reviews, Vol. 47 (4), 2005)
"In recent time optimal control in finance is connected with modelling of stock prices by Lévy processes and considering of different transaction costs. In the last ten years the authors and their collaborators obtained a lot of results on this field. The publication of this work in the present book seems to be a good way to attain a big audience. . It is useful for students and practitioners in stochastic analysis." (Hans-Joachim Girlich, OR News, Issue 25, November, 2005)
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