Reflected BSDEs with regulated trajectories

TL;DR

This paper studies reflected backward stochastic differential equations with regulated trajectories, proving existence, uniqueness, and approximation methods, and applying these results to optimal stopping problems.

Contribution

It introduces solutions for reflected BSDEs with regulated trajectories, including a novel penalization approximation method and applications to optimal stopping.

Findings

Existence and uniqueness of solutions established.

Solution can be approximated via a modified penalization method.

Application demonstrated in an optimal stopping problem.

Abstract

We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the solution may be approximated by a modified penalization method. Application to an optimal stopping problem is given.