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

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
External document link
http://hal.archives-ouvertes.fr/hal-00615501/fr/
Date
2011
Publisher
université Paris-Dauphine
Published in
Paris
Pages
34
Metadata
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Author(s)
Réveillac, Anthony
Abstract (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.
Subjects / Keywords
continuous Markov martingale; differentiability of BSDEs; existence of quadratic BSDEs; Martingale representation

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