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dc.contributor.authorPossamaï, Dylan
dc.contributor.authorZhou, Chao
dc.date.accessioned2015-04-07T11:36:44Z
dc.date.available2015-04-07T11:36:44Z
dc.date.issued2013
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14888
dc.language.isoenen
dc.subjectSecond order backward stochastic differential equationen
dc.subjectQuadratic growthen
dc.subjectBMO martingalesen
dc.subjectr.c.p.d.en
dc.subjectFeynman–Kacen
dc.subjectFully non-linear PDEsen
dc.subjectQuasi-sureen
dc.subject.ddc519en
dc.titleSecond order backward stochastic differential equations with quadratic growthen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012) [31] to the case of a bounded terminal condition and a generator with quadratic growth in the zz variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman–Kac formula and a probabilistic representation for fully non-linear PDEs in this setting.en
dc.relation.isversionofjnlnameStochastic Processes and their Applications
dc.relation.isversionofjnlvol123en
dc.relation.isversionofjnlissue10en
dc.relation.isversionofjnldate2013
dc.relation.isversionofjnlpages3770-3799en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.spa.2013.05.007en
dc.identifier.urlsitehttp://arxiv.org/abs/1201.1050v4en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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