Reflected Backward SDEs with General Jumps

Abstract

We study one-dimensional reflected backward stochastic differential equations (BSDEs) driven by a Brownian motion and an independent Poisson random measure when the generator is Lipschitz. We first derive existence and uniqueness of the solution of reflected BSDEs with one reflecting barrier when the obstacle process is right continuous with left limits (RCLL) and has arbitrary jump structure. We then rely on Mokobodski's condition to show existence and uniqueness of the solution of reflected BSDEs with two RCLL reflecting barriers.