$\boldsymbol{\mathbb{L}^p(p\ge2)}$-solutions of generalized BSDEs with jumps and monotone generator in a general filtration

TL;DR

This paper establishes existence, uniqueness, and comparison results for multidimensional generalized backward stochastic differential equations with jumps and monotone generators in a broad filtration setting, extending to random terminal times.

Contribution

It provides new existence and uniqueness theorems for $ ext{L}^p$-solutions of BSDEs with jumps in a general filtration, including cases with random terminal times.

Findings

Proved existence and uniqueness of $ ext{L}^p$-solutions for fixed terminal time.

Extended results to cases with random terminal times.

Established a comparison theorem in one dimension.

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 $\mathbb{L}^p(p\ge2)$-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 $1$.