Malliavin Calculus for Levy Processes with Applications to Finance (häftad)
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Häftad (Paperback / softback)
Antal sidor
1st Corrected ed. 2009, Corr. 2nd printing 2009
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
ksendal, Bernt / Proske, Frank
XIV, 418 p.
235 x 155 x 25 mm
659 g
Antal komponenter
1 Paperback / softback
Malliavin Calculus for Levy Processes with Applications to Finance (häftad)

Malliavin Calculus for Levy Processes with Applications to Finance

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Häftad Engelska, 2008-09-17
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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.
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From the reviews: "The book under review gives a quite complete description of the Malliavin and white noise approaches to stochastic analysis on both the Wiener and Poisson spaces with applications to mathematical finance. ... In addition each chapter is accompanied with exercises and their solutions. ... The technical requirements of the book are kept at a reasonable level and its organisation into short chapters not only facilitates the reading but also provides several alternative study plans making it a valuable learning and reference tool." (Nicolas Privault, Mathematical Reviews, Issue 2010 f)

Övrig information

Giulia Di Nunno, Bernt Oksendal and Frank Proske are professors at the Department of Mathematics, University of Oslo, Norway. The three scholars are active in the fields of stochastic analysis, mathematical and quantitative finance.


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.