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

Badr Elmansouri

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

Probability 2025-08-12 v1

Authors: Badr Elmansouri

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.

Keywords

BSDE reflected BSDE L^p solution jump processes stochastic Lipschitz

Cite

@article{arxiv.2508.07039,
  title  = {$\mathbb{L}^p$-solutions for BSDEs and Reflected BSDEs with jumps in a general filtration under stochastic Lipschitz coefficient},
  author = {Badr Elmansouri},
  journal= {arXiv preprint arXiv:2508.07039},
  year   = {2025}
}

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