Reflected and doubly reflected BSDEs for Lévy processes: Solutions and comparison

Abstract

In this paper we study reflected and doubly reflected backward stochastic differential equations (BSDEs, for short) driven by Teugels martingales associated with Levy process satisfying some moment conditions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the Tanaka-Meyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski’s condition by using the Snell envelope theory and then we obtain a comparison result.