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

TL;DR

This paper studies multidimensional backward stochastic differential equations with monotone generators driven by Brownian motion and Poisson noise, establishing existence, uniqueness, and comparison results under integrability conditions.

Contribution

It extends existing results to multidimensional BSDEs with jumps in a general filtration, including random time horizons and a comparison principle in one dimension.

Findings

Proved existence and uniqueness of solutions in $L^p$.

Extended results to random time horizons.

Provided a comparison principle in one dimension.

Abstract

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.