Malliavin calculus for Lévy processes with applications to finance
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Bibliographic Information
Malliavin calculus for Lévy processes with applications to finance
（Universitext）
Springer, c2009
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Note
Includes bibliographical references (p. 395-406) and index
Description and Table of Contents
Description
There are already several excellent books on Malliavin calculus. However, most of them deal only with the theory of Malliavin calculus for Brownian motion, with [35] as an honorable exception. Moreover, most of them discuss only the applicationto regularityresults for solutions ofSDEs, as this wasthe original motivation when Paul Malliavin introduced the in?nite-dimensional calculus in 1978 in [158]. In the recent years, Malliavin calculus has found many applications in stochastic control and within ?nance. At the same time, L' evy processes have become important in ?nancial modeling. In view of this, we have seen the need for a book that deals with Malliavin calculus for L' evy processesin general,not just Brownianmotion, and that presentssome of the most important and recent applications to ?nance. It is the purpose of this book to try to ?ll this need. In this monograph we present a general Malliavin calculus for L' evy processes, covering both the Brownianmotioncaseand the purejump martingalecasevia Poissonrandom measures,and also some combination of the two.
Table of Contents
The Continuous Case: Brownian Motion.- The Wiener-Ito Chaos Expansion.- The Skorohod Integral.- Malliavin Derivative via Chaos Expansion.- Integral Representations and the Clark-Ocone formula.- White Noise, the Wick Product, and Stochastic Integration.- The Hida-Malliavin Derivative on the Space ? = S?(?).- The Donsker Delta Function and Applications.- The Forward Integral and Applications.- The Discontinuous Case: Pure Jump Levy Processes.- A Short Introduction to Levy Processes.- The Wiener-Ito Chaos Expansion.- Skorohod Integrals.- The Malliavin Derivative.- Levy White Noise and Stochastic Distributions.- The Donsker Delta Function of a Levy Process and Applications.- The Forward Integral.- Applications to Stochastic Control: Partial and Inside Information.- Regularity of Solutions of SDEs Driven by Levy Processes.- Absolute Continuity of Probability Laws.
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