Applied Stochastic Control of Jump Diffusions
Description
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 3 rd edition is an expanded and updated version of the 2 nd 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.Reviews / Votes
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 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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Persons
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.
Content
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.