Reflected BSDEs driven by inhomogeneous simple Lévy processes with RCLL barrier

Abstract

We study the solution of a backward stochastic differential equation driven by an inhomogeneous simple Lévy process with a rcll reflecting barrier. We show the existence and uniqueness of solution by means of the Snell envelope and the fixed point theorem when the coefficient is stochastic Lipschitz. In terms of application, we provide the fair price of the American option in a Lévy market.