$\mathbb {L}^p(p\ge 2)$-solutions of generalized BSDEs with jumps and monotone generator in a general filtration

Abstract

In this paper, we study multidimensional generalized BSDEs that have a monotone generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. First, we prove the existence and uniqueness of Lp(p≥2)-solutions in the case of a fixed terminal time under suitable p--integrability conditions on the data. Then, we extend these results to the case of a random terminal time. Furthermore, we provide a comparison result in dimension 1.