BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration

T Kruse (1) , A Popier (2)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 LMM - Laboratoire Manceau de Mathématiques

We analyze multidimensional BSDEs in a filtration that supports a Brownian motion and a Poisson random measure. Under a monotonicity assumption on the driver, the paper extends several results from the literature. We establish existence and uniqueness of solutions in $L^p$ provided that the generator and the terminal condition satisfy appropriate integrability conditions. The analysis is first carried out under a deterministic time horizon, and then generalized to random time horizons given by a stopping time with respect to the underlying filtration. Moreover, we provide a comparison principle in dimension one.

Domaines: Probabilités [math.PR]

T Kruse, A Popier. BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. 2015. ⟨hal-01094836v3⟩