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Applied Stochastic Control of Jump Diffusions

  • Bernt Øksendal
  • Agnès Sulem
Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Bernt Øksendal, Agnès Sulem
    Pages 1-26
  3. Bernt Øksendal, Agnès Sulem
    Pages 27-53
  4. Bernt Øksendal, Agnès Sulem
    Pages 55-73
  5. Bernt Øksendal, Agnès Sulem
    Pages 75-91
  6. Bernt Øksendal, Agnès Sulem
    Pages 93-155
  7. Bernt Øksendal, Agnès Sulem
    Pages 157-210
  8. Bernt Øksendal, Agnès Sulem
    Pages 211-223
  9. Bernt Øksendal, Agnès Sulem
    Pages 225-237
  10. Bernt Øksendal, Agnès Sulem
    Pages 239-254
  11. Bernt Øksendal, Agnès Sulem
    Pages 255-272
  12. Bernt Øksendal, Agnès Sulem
    Pages 273-283
  13. Bernt Øksendal, Agnès Sulem
    Pages 285-312
  14. Bernt Øksendal, Agnès Sulem
    Pages 343-415
  15. Back Matter
    Pages 417-436

About this book

Introduction

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.

Keywords

47J20, 49J40, 60G40, 65M06, 65M12, 91A23, 91B28, 91GXX, 93E20 Lévy Processes Jump Diffusions Stochastic Control Financial Markets Modelled by Jump Diffusions Backward Stochastic Differential Equations Convex Risk Measures Optimal Stopping Impulse Control Stochastic Differential Games Partial Information Control Forward-Backward SDEs Mean-Field SDEs Optimal Control of SPDEs

Authors and affiliations

  • Bernt Øksendal
    • 1
  • Agnès Sulem
    • 2
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Inria Research Center of ParisParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02781-0
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02779-7
  • Online ISBN 978-3-030-02781-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site