Reflected backward stochastic differential equations with two optional barriers

TL;DR

This paper studies reflected backward stochastic differential equations with two optional barriers, establishing existence, uniqueness, and approximation methods for solutions with regulated trajectories.

Contribution

It introduces a framework for solving RBSDEs with two optional barriers, proving existence, uniqueness, and approximation via penalization.

Findings

Existence and uniqueness of solutions for RBSDEs with two optional barriers.

Solutions have regulated trajectories with finite left and right limits.

Solutions can be approximated using a modified penalization method.

Abstract

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove the existence and uniqueness of $\mathbb L^p$ solutions, $p\geq 1$, and show that the solutions may be approximated by a modified penalization method.