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Stochastic control with rough paths

dc.contributor.authorDiehl, Joscha
dc.contributor.authorFriz, Peter K.
dc.contributor.authorGassiat, Paul
dc.date.accessioned2017-03-09T16:02:19Z
dc.date.available2017-03-09T16:02:19Z
dc.date.issued2017
dc.identifier.issn1432-0606
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16316
dc.language.isoenen
dc.subjectStochastic control
dc.subjectDuality
dc.subjectRough paths
dc.subject.ddc519en
dc.titleStochastic control with rough paths
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
dc.relation.isversionofjnlnameApplied Mathematics & Optimization
dc.relation.isversionofjnlvol75
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages285-315
dc.relation.isversionofdoi10.1007/s00245-016-9333-9
dc.identifier.urlsitehttps://arxiv.org/abs/1303.7160v2
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewednon
dc.date.updated2017-03-22T14:34:19Z


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