Reflected Backward Stochastic Differential Equations Driven by L\'{e}vy Process

TL;DR

This paper studies reflected backward stochastic differential equations driven by Lévy processes, establishing existence and uniqueness of solutions and linking them to partial differential-integral inclusions.

Contribution

It introduces a new class of reflected backward stochastic differential equations driven by Lévy processes and proves their well-posedness using penalization methods.

Findings

Existence and uniqueness of solutions are established.

Provides a probabilistic interpretation for certain partial differential-integral inclusions.

Extends the theory of backward stochastic differential equations to Lévy-driven settings.

Abstract

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy process. We obtain the existence and uniqueness of solutions to these equations by means of the penalization method. As its application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.