Backward stochastic differential equations driven by G-Lévy process with double reflexions

Abstract

Abstract In this paper, we study the reflected backward stochastic differential equations driven by G-Lévy process with two reflecting obstacles under the Lipschitz condition on the coefficients, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condition is proposed to derive the uniqueness and existence of the solutions. We give some a priori estimations for the uniqueness and we prove the existence of the solution by penalization method.