Applied Stochastic Control of Jump Diffusions

  • Bernt Øksendal
  • Agnès Sulem

Part of the Universitext book series (UTX)

About this book

Introduction

The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.

The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the 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. There are also chapters on the viscosity solution formulation and numerical methods.

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.

In the 2nd edition there is a new chapter on optimal control of stochastic partial differential equations driven by Lévy processes. There is also a new section on optimal stopping with delayed information. Moreover, corrections and other improvements have been made.

Keywords

Lévy process Lévy processes Stochastic calculus impulse control jump diffusion jump diffusions linear optimization measure theory stochastic control

Authors and affiliations

  • Bernt Øksendal
    • 1
  • Agnès Sulem
    • 2
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Domaine de VoluceauINRIA RocquencourtLe Chesnay CXFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69826-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-69825-8
  • Online ISBN 978-3-540-69826-5
  • About this book