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Malliavin Calculus for Levy Processes with Applications to Finance - pr_18635

Malliavin Calculus for Levy Processes with Applications to Finance

By Giulia Di Nunno, Bernt Oksendal, Frank Proske

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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.

Product code: 9783540785712

ISBN 9783540785712
Dimensions (HxWxD in mm) H235xW155
Series Universitext
No. Of Pages 418
Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition 1st Corrected ed. 2009, Corr. 2nd printing 2009
This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.