Reflected backward stochastic differential equations with optional barriers: monotone approximation

TL;DR

This paper studies reflected backward stochastic differential equations with optional barriers, focusing on existence, approximation via decreasing limits of cadlag barriers, and their relation to standard cadlag BSDEs.

Contribution

It introduces a method to construct solutions for RBSDEs with optional barriers using decreasing limits of cadlag barriers and compares these with classical cadlag BSDEs.

Findings

Solutions exist under the given conditions.

Approximation via decreasing limits is effective.

Connections to classical cadlag BSDEs are established.

Abstract

In this short note we consider RBSDE with Lipschitz drivers and barrier processes that are optional and right upper semicontinuous. We treat the case when the barrier can be represented as a decreasing limit of cadlag barriers. We combine well known existence results for cadlag barriers with comparison arguments for the control process to construct solutions. Finally, we highlight the connection of such RBSDEs with usual cadlag BSDEs.