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dc.contributor.authorBouchard, Bruno
dc.date.accessioned2010-02-18T10:37:08Z
dc.date.available2010-02-18T10:37:08Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3497
dc.language.isoenen
dc.subjectStochastic Target Problem
dc.subjectdiscontinuous viscosity solutions
dc.subjectOptimal Control
dc.subjectState Constraint Problem
dc.subject.ddc519en
dc.titleOptimal Control under Stochastic Target Constraints
dc.typeCommunication / Conférence
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.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.conftitleSymposium on Optimal Stopping with Applications
dc.relation.confcityTurku
dc.relation.confcountryFINLAND
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-22T09:23:36Z


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