Research Catalog

Applied stochastic control of jump diffusions

Title
  1. Applied stochastic control of jump diffusions / Bernt Oksendal, Agnès Sulem.
Published by
  1. Berlin ; New York : Springer, ©2005.
Author
  1. Øksendal, B. K. (Bernt Karsten), 1945-

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Details

Additional authors
  1. Sulem, Agnès.
Description
  1. x, 208 pages : illustrations; 24 cm
Summary
  1. "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 is also a chapter 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."--Jacket.
Series statement
  1. Universitext
Uniform title
  1. Universitext
Subject
  1. Stochastic control theory
  2. Stochastic processes
  3. Viscosity solutions
  4. Stochastic Processes
  5. Diffusionsprozess
  6. Lévy-Prozess
  7. Sprungprozess
  8. Stochastische Kontrolltheorie
  9. Stochastische processen
  10. Controleleer
Contents
  1. Stochastic calculus with jump diffusions -- Optimal stopping of jump diffusions -- Stochastic control of jump diffusions -- Combined optimal stopping and stochastic control of jump diffusions -- Impulse control of jump diffusions -- Approximating impulse control of diffusions by iterated optimal stopping -- Combined stochastic control and impulse control of jump diffusions -- Singular control of jump diffusions -- Viscosity solutions -- Numerical solutions methods -- Appendices: Solutions of the exercises.
Owning institution
  1. Princeton University Library
Bibliography (note)
  1. Includes bibliographical references (p. [197]-201) and index.