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Pré-Publication, Document De Travail Année : 2011

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

Résumé

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.
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Dates et versions

hal-00615501 , version 1 (19-08-2011)

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Anthony Réveillac. Weak martingale representation for continuous Markov processes and application to quadratic growth BSDEs. 2011. ⟨hal-00615501⟩
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