dc.contributor.author Bouchard, Bruno dc.contributor.author Elie, Romuald dc.contributor.author Imbert, Cyril dc.date.accessioned 2009-09-25T12:47:21Z dc.date.available 2009-09-25T12:47:21Z dc.date.issued 2010 dc.identifier.issn 0363-0129 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/1961 dc.language.iso en en dc.subject Stochastic Target Problem dc.subject discontinuous viscosity solutions dc.subject State Constraint Problem dc.subject Optimal Control dc.subject.ddc 519 en dc.title Optimal Control under Stochastic Target Constraints dc.type Article accepté pour publication ou publié dc.description.abstracten We 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.isversionofjnlname SIAM Journal on Control and Optimization dc.relation.isversionofjnlvol 48 dc.relation.isversionofjnlissue 5 dc.relation.isversionofjnldate 2010 dc.relation.isversionofjnlpages 3501-3531 dc.relation.isversionofdoi http://dx.doi.org/10.1137/090757629 dc.description.sponsorshipprivate oui en dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2017-09-22T16:50:56Z
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