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dc.contributor.authorBouchard, Bruno
dc.contributor.authorElie, Romuald
dc.contributor.authorTouzi, Nizar
dc.date.accessioned2009-09-25T11:47:11Z
dc.date.available2009-09-25T11:47:11Z
dc.date.issued2009
dc.identifier.issn0363-0129
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1953
dc.language.isoenen
dc.subjectDiscontinuous Viscosity Solutions
dc.subjectStochastic target problem
dc.subjectQuantile Hedging
dc.subject.ddc519en
dc.titleStochastic target problems with controlled loss
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider the problem of finding the minimal initial data of a controlled processwhich guarantees to reach a controlled target with a given probability of success or, more generally,with a given level of expected loss. By suitably increasing the state space and the controls, weshow that this problem can be converted into a stochastic target problem, i.e., finding the minimalinitial data of a controlled process which guarantees to reach a controlled target with probability one.Unlike in the existing literature on stochastic target problems, our increased controls are valued in anunbounded set. In this paper, we provide a new derivation of the dynamic programming equation forgeneral stochastic target problems with unbounded controls, together with the appropriate boundaryconditions. These results are applied to the problem of quantile hedging in financial mathematicsand are shown to recover the explicit solution of F¨ ollmer and Leukert [Finance Stoch., 3 (1999), pp.251–273].
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol48
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2009
dc.relation.isversionofjnlpages3123-3150
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/08073593X
dc.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-09-22T16:52:16Z


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