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Stochastic control for a class of nonlinear kernels and applications

dc.contributor.authorPossamaï, Dylan
dc.contributor.authorTan, Xiaolu
dc.contributor.authorZhou, Chao
dc.date.accessioned2018-01-15T15:43:10Z
dc.date.available2018-01-15T15:43:10Z
dc.date.issued2018
dc.identifier.issn0091-1798
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17343
dc.language.isoenen
dc.subjectStochastic control
dc.subjectmeasurable selection
dc.subjectnon-linear kernels
dc.subjectsecond order
dc.subjectBSDEs
dc.subjectpath-dependent PDEs
dc.subjectrobust superhedging
dc.subject.ddc519en
dc.titleStochastic control for a class of nonlinear kernels and applications
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimization, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are non-linear generalizations of the traditional (linear) expectations, this problem can be understood as stochastic control of a family of nonlinear expectations, or equivalently of nonlinear kernels. Our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting, which we then use to provide a semimartingale characterization of the value function. We next explore several applications of our results. We first obtain a wellposedness result for second order BSDEs (as introduced in [76]) which does not require any regularity assumption on the terminal condition and the generator. Then we prove a non-linear optional decomposition in a robust setting, extending recent results of [63], which we then use to obtain a superhedging duality in uncertain, incomplete and non-linear financial markets. Finally, we relate, under additional regularity assumptions, the value function to a viscosity solution of an appropriate path-dependent partial differential equation (PPDE).
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol46
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages551-603
dc.relation.isversionofdoi10.1214/17-AOP1191
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingouien
dc.relation.forthcomingprintouien
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-03-16T08:47:30Z


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