Penalization method for reflected BDSDEs with two-sided jumps and driven by L\'evy process

TL;DR

This paper establishes the existence and uniqueness of solutions for a class of reflected backward doubly stochastic differential equations driven by Le9vy processes, using a novel penalization approach to handle non-right-continuous barriers.

Contribution

It introduces a new penalization method to prove existence and uniqueness for reflected BDSDEs with non-right-continuous barriers driven by Le9vy processes.

Findings

Proved existence and uniqueness of solutions.

Developed a new penalization technique.

Handled non-right-continuous barriers.

Abstract

In this paper, we prove the existence and uniqueness of the solution to reflected backward doubly stochastic differential equations driven by Teugels martingales associated with a L\'evy process where the barrier process is not necessarily right continuous by approximating such equations by a new version of penalization method.