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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBouchard, Bruno*
hal.structure.identifier
dc.contributor.authorLoeper, Grégoire*
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dc.contributor.authorSoner, Halil Mete*
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dc.contributor.authorZhou, Chao*
dc.date.accessioned2018-09-03T11:44:47Z
dc.date.available2018-09-03T11:44:47Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17924
dc.language.isoenen
dc.subjectstochastic target problems
dc.subjectgeneral market impacts
dc.subject.ddc519en
dc.titleSecond order stochastic target problems with generalized market impact
dc.typeDocument de travail / Working paper
dc.description.abstractenWe extend the study of [7, 18] to stochastic target problems with general market impacts. Namely, we consider a general abstract model which can be associated to a fully nonlinear parabolic equation. Unlike [7, 18], the equation is not concave and the regularization/verification approach of [7] can not be applied. We also relax the gamma constraint of [7]. In place, we need to generalize the a priori estimates of [18] and exhibit smooth solutions from the classical parabolic equations theory. Up to an additional approximating argument, this allows us to show that the super-hedging price solves the parabolic equation and that a perfect hedging strategy can be constructed when the coefficients are smooth enough. This representation leads to a general dual formulation. We finally provide an asymptotic expansion around a model without impact.
dc.identifier.citationpages27
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2019-10-03T09:55:12Z
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