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Malliavin Calculus for Levy Processes with Applications to Finance (Paperback, 1st Corrected ed. 2009, Corr. 2nd printing 2009)
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Malliavin Calculus for Levy Processes with Applications to Finance (Paperback, 1st Corrected ed. 2009, Corr. 2nd printing 2009)
Series: Universitext
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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.
General
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