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dc.contributor.authorBouchard, Bruno
dc.contributor.authorElie, Romuald
dc.contributor.authorImbert, Cyril
dc.date.accessioned2009-09-25T12:47:21Z
dc.date.available2009-09-25T12:47:21Z
dc.date.issued2010
dc.identifier.issn0363-0129
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1961
dc.language.isoenen
dc.subjectStochastic Target Problem
dc.subjectdiscontinuous viscosity solutions
dc.subjectState Constraint Problem
dc.subjectOptimal Control
dc.subject.ddc519en
dc.titleOptimal Control under Stochastic Target Constraints
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study a class of Markovian optimal stochastic control problems in which the controlled process $Z^\nu$ is constrained to satisfy an a.s.~constraint $Z^\nu(T)\in G\subset \R^{d+1}$ $\Pas$ at some final time $T>0$. When the set is of the form $G:=\{(x,y)\in \R^d\x \R~:~g(x,y)\ge 0\}$, with $g$ non-decreasing in $y$, we provide a Hamilton-Jacobi-Bellman characterization of the associated value function. It gives rise to a state constraint problem where the constraint can be expressed in terms of an auxiliary value function $w$ which characterizes the set $D:=\{(t,Z^\nu(t))\in [0,T]\x\R^{d+1}~:~Z^\nu(T)\in G\;a.s.$ for some $ \nu\}$. Contrary to standard state constraint problems, the domain $D$ is not given a-priori and we do not need to impose conditions on its boundary. It is naturally incorporated in the auxiliary value function $w$ which is itself a viscosity solution of a non-linear parabolic PDE. Applying ideas recently developed in Bouchard, Elie and Touzi (2008), our general result also allows to consider optimal control problems with moment constraints of the form $\Esp{g(Z^\nu(T))}\ge 0$ or $\Pro{g(Z^\nu(T))\ge 0}\ge p$.
dc.relation.isversionofjnlnameSIAM Journal on Control and Optimization
dc.relation.isversionofjnlvol48
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages3501-3531
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/090757629
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.updated2017-09-22T16:50:56Z


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