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Applied Stochastic Control of Jump Diffusions / Edition 1

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Berlin, Germany 2004 Trade paperback New. Trade paperback (US). Glued binding. 208 p. Universitext.

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Overview

Here is a rigorous introduction to the most important and useful solution methods of various types of shastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of shastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of shastic analysis, measure theory and partial differential equations is assumed.

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Editorial Reviews

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From the reviews:

"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 shastic 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 shastic 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 shastic control literature … ." (Jose-Luis Menaldi, SIAM Reviews, Vol. 47 (4), 2005)

"In recent time optimal control in finance is connected with modelling of sk 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 shastic analysis." (Hans-Joachim Girlich, OR News, Issue 25, November, 2005)

From the reviews of the second edition:

“The book is a research monograph … . book includes many worked examples (and several more are unsolved exercises) that will serve the dedicated student in good stead. … In summary, this is a good and relatively inexpensive book that should appeal to graduate students and researchers with some prior knowledge of shastic control who now wish to learn about the jump diffusion case––especially, as applied in the areas of computational finance and economics.” (S. Ramamoorthy, Journal of the Operational Research Society, Vol. 62, 2011)

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Product Details

  • ISBN-13: 9783540140238
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 12/22/2004
  • Series: Universitext Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 208
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.50 (d)

Table of Contents

Shastic calculus with jump diffusions.- Optimal stopping of jump diffusions.- Shastic control of jump diffusions.- Combined optimal stopping and shastic control of jump diffusions.- Impulse control of jump diffusions.- Approximating impulse control of diffusions by iterated optimal stopping.- Combined shastic control and impulse control of jump diffusions.- Singular control of jump diffusions.- Viscosity solutions.- Numerical solutions methods.- Appendices: Solutions of the exercises.- Bibliography.- List of frequently used notation and symbols.- Index.

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