Applied Stochastic Control of Jump Diffusions (Universitext) - Softcover

Øksendal, Bernt; Sulem, Agnès

Softcover

ISBN 10: 3540140239 ISBN 13: 9783540140238

Verlag: Springer, 2004

Inhaltsangabe

This book offers 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 extends to both the dynamic programming method and the maximum principle method, as well as the relation between them. The authors formulate the corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities. The text emphasises real-world applications, primarily in the field of finance. All the main results are illustrated by examples, and exercises appear at the end of each chapter with complete solutions, to help the reader understand the theory and learn how to apply it. The 2nd edition adds a new chapter on optimal control of stochastic partial differential equations driven by Lévy processes, along with a new section on optimal stopping with delayed information. Some basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

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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 (i.e. solutions of stochastic differential equations driven by Lévy processes) 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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2004
• Sprache: Englisch
• ISBN 10: 3540140239
• ISBN 13: 9783540140238
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 224
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland