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Weak martingale representation for continuous Markov processes and application to quadratic growth BSDEs

dc.contributor.authorRéveillac, Anthony
HAL ID: 745074
dc.date.accessioned2011-08-29T13:45:00Z
dc.date.available2011-08-29T13:45:00Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6873
dc.language.isoenen
dc.subjectcontinuous Markov martingaleen
dc.subjectdifferentiability of BSDEsen
dc.subjectexistence of quadratic BSDEsen
dc.subjectMartingale representationen
dc.subject.ddc519en
dc.titleWeak martingale representation for continuous Markov processes and application to quadratic growth BSDEsen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper we prove that every random variable of the form $F(M_T)$ with $F:\real^d \to\real$ a Borelian map and $M$ a $d$-dimensional continuous Markov martingale with respect to a Markov filtration $\mathcal{F}$ admits an exact integral representation with respect to $M$, that is, without any orthogonal component. This representation holds true regardless any regularity assumption on $F$. We extend this result to Markovian quadratic growth BSDEs driven by $M$ and show they can be solved without an orthogonal component. To this end, we extend first existence results for such BSDEs under a general filtration and then obtain regularity properties such as differentiability for the solution process.en
dc.publisher.nameuniversité Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages34en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00615501/fr/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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