BSDEs with monotone generator and two irregular reflecting barriers

TL;DR

This paper studies backward stochastic differential equations (BSDEs) with two irregular reflecting barriers, establishing conditions for solutions' existence, uniqueness, and approximation methods in the context of monotone generators and irregular barriers.

Contribution

It provides necessary and sufficient conditions for the existence and uniqueness of solutions to BSDEs with irregular barriers and monotone generators, extending previous results to more complex settings.

Findings

Established existence and uniqueness criteria for solutions.

Proved solutions can be approximated via penalization methods.

Extended theory to irregular barriers and monotone generators.

Abstract

We consider BSDEs with two reflecting irregular barriers. We give necessary and sufficient conditions for existence and uniqueness of $\mathbb{L}^{p}$ solutions for equations with generators monotone with respect to $y$ and Lipschitz continuous with respect to $z$, and with data in $\mathbb{L}^{p}$ spaces for $p\ge 1$. We also prove that the solutions can be approximated via penalization method.