Reflected BSDEs with general filtration and two completely separated barriers

TL;DR

This paper establishes the existence and uniqueness of solutions for reflected backward stochastic differential equations with two separated barriers on general filtrations, and applies these results to zero-sum Dynkin games.

Contribution

It extends the theory of reflected BSDEs to general filtrations with separated barriers, providing new existence and uniqueness results under minimal assumptions.

Findings

Proved existence and uniqueness of solutions for reflected BSDEs with separated barriers.

Extended the theory to general filtrations beyond the usual Brownian setting.

Applied the results to analyze zero-sum Dynkin games.

Abstract

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we assume that there are c\`adl\`ag processes of class D that are completely separated. We prove the existence and uniqueness of solutions for integrable final condition and integrable monotone generator. An application to zero-sum Dynkin game is given.