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dc.contributor.authorLions, Pierre-Louis
dc.contributor.authorLebuchoux, Jérôme
dc.contributor.authorLasry, Jean-Michel
dc.contributor.authorFournié, Eric
dc.date.accessioned2011-04-19T10:50:56Z
dc.date.available2011-04-19T10:50:56Z
dc.date.issued2001
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6013
dc.language.isoenen
dc.subjectfunctional dependenceen
dc.subjectanticipative Girsanov transformen
dc.subjectPDEen
dc.subjectconditional expectationsen
dc.subjecthedge ratios and greeksen
dc.subjectMalliavin calculusen
dc.subjectMonte Carlo methodsen
dc.subject.ddc519en
dc.subject.classificationjelG13en
dc.subject.classificationjelC63en
dc.titleApplications of Malliavin calculus to Monte-Carlo methods in finance. IIen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis paper is the sequel of Part I [1], where we showed how to use the so-called Malliavin calculus in order to devise efficient Monte-Carlo (numerical) methods for Finance. First, we return to the formulas developed in [1] concerning the “greeks” used in European options, and we answer to the question of optimal weight functional in the sense of minimal variance. Then, we investigate the use of Malliavin calculus to compute conditional expectations. The integration by part formula provides a powerful tool when used in the framework of Monte Carlo simulation. It allows to compute everywhere, on a single set of trajectories starting at one point, solution of general options related PDEs. Our final application of Malliavin calculus concerns the use of Girsanov transforms involving anticipating drifts. We give an example in numerical Finance of such a transform which gives reduction of variance via importance sampling. Finally, we include two appendices that are concerned with the PDE interpretation of the formulas presented in [1] for the delta of a European option and with the connections between the functional dependence of some random variables and their Malliavin derivatives.en
dc.relation.isversionofjnlnameFinance and Stochastics
dc.relation.isversionofjnlvol5en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2001
dc.relation.isversionofjnlpages201-236en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/PL00013529en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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