Reflected BSDEs with two completely separated barriers and regulated trajectories in general filtration

TL;DR

This paper establishes the existence and uniqueness of solutions for doubly reflected backward stochastic differential equations with separated barriers in general filtrations lacking regularity assumptions.

Contribution

It extends the theory of reflected BSDEs to cases with non-regular, separated barriers under minimal filtration assumptions, without requiring right continuity.

Findings

Proves existence and uniqueness of solutions under minimal assumptions.

Handles barriers with no regularity or right continuity.

Shows solutions exist when barriers are completely separated.

Abstract

In this paper, we study doubly reflected Backward Stochastic Differential Equations defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness in the case where the barriers L and U don't satisfy any regularity assumption (without right continuity). We suppose that the barriers L and U and their left limits are completely separated and we show existence and uniqueness of the solution.