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. From the reviews:
"The book is very well written, and will undoubtedly remain a major reference on the topic for years to come. It is an authoritative book which should be of interest to researchers in stochastic control, mathematical finance and applied mathematics. ... One of the main distinguishing features of this book is that it provides plenty of interesting exercises originated from financial market. It is very helpful for both beginners. I wish I had done these exercise when I was a student!" (Lu Qi, zbMATH 1422.93001, 2019)
"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 Levy processes and considering of different transaction costs. In the last ten years the authors and their collaborators obtained a lot of results on this fie
Applied Stochastic Control of Jump Diffusions
Preface.- Stochastic Calculus with Levy Processes.- Financial Markets Modelled by Jump Diffusions.- Optimal Stopping of Jump Diffusions.- Backward Stochastic Differential Equations and Risk Measures.- Stochastic Control of Jump Diffusions.- Stochastic Differential Games.- Combined Optimal Stopping and Stochastic Control of Jump Diffusions.- Viscosity Solutions.- Solutions of Selected Exercises.- References.- Notation and Symbols.