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

Réveillac, Anthony

Réveillac, Anthony (2011), Weak martingale representation for continuous Markov processes and application to quadratic growth BSDEs. https://basepub.dauphine.fr/handle/123456789/6873

Type

Document de travail / Working paper

Lien vers un document non conservé dans cette base

http://hal.archives-ouvertes.fr/hal-00615501/fr/

Date

2011

Éditeur

université Paris-Dauphine

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Réveillac, Anthony

Résumé (EN)

In 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.

Mots-clés

continuous Markov martingale; differentiability of BSDEs; existence of quadratic BSDEs; Martingale representation