$\mathbb{L}^p$-solutions for BSDEs and Reflected BSDEs with jumps in a general filtration under stochastic Lipschitz coefficient

TL;DR

This paper establishes existence and uniqueness of  solutions for BSDEs and reflected BSDEs with jumps in a general filtration, under stochastic Lipschitz conditions and  integrability.

Contribution

It extends  theory to general filtrations with jumps under stochastic Lipschitz conditions, covering both BSDEs and reflected BSDEs.

Findings

Proves existence and uniqueness of  solutions.

Handles general filtration with Brownian motion and Poisson jumps.

Includes reflected BSDEs with RCLL barriers.

Abstract

In this paper, we study the existence and uniqueness of $\mathbb{L}^p$-solutions for $p \in (1, 2)$, first for backward stochastic differential equations (BSDEs) in a general filtration that supports a Brownian motion and an independent Poisson random measure, and then for reflected BSDEs with an RCLL barrier in the same stochastic framework. The results are obtained under suitable $\mathbb{L}^p$-integrability conditions on the data and a stochastic-Lipschitz condition on the coefficient.