| 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 | |
