The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications. Both the dynamic programming method and the stochastic maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi-Bellman equation and/or (quasi-)variational inequalities are formulated. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. The 3rd edition is an expanded and updated version of the 2nd edition, containing recent developments within stochastic control and its applications. Specifically, there is a new chapter devoted to a comprehensive presentation of financial markets modelled by jump diffusions, and one on backward stochastic differential equations and convex risk measures. Moreover, the authors have expanded the optimal stopping and the stochastic control chapters to include optimal control of mean-field systems and stochastic differential games.

Autorentext

Agnès Sulem is a researcher at INRIA, Paris. She leads the MATHRISK research group and the Premia consortium for quantitative finance. She teaches in the doctoral programs at University Paris-Dauphine and Luxemburg University. Her fields of research are stochastic control, numerical and stochastic analysis, and mathematical finance. She is the author of 2 books and about 100 research articles. Besides mathematics, Agnès Sulem enjoys playing the violin.

Bernt Øksendal is professor emeritus at the University of Oslo (UiO) and associate professor and Honorary Doctor at the Norwegian School of Economics (NHH). He was awarded the Nansen Prize in 1996 and the UiO Research Prize in 2014. His interests are in stochastic analysis, stochastic control and applications, especially in biology and finance. He has over 200 publications, including 10 books. His other interests and pleasures include jogging, music, science and nature.

Klappentext

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.

Inhalt

Preface.- Stochastic Calculus with Lévy 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.