Reflected BSDEs with general filtration and two completely separated barriers

Abstract

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness. As for barriers we assume that there are c\`adl\`ag processes of class D that are completely separated. We prove the existence and uniqueness of solutions for integrable final condition and integrable monotone generator. An application to zero-sum Dynkin game is given.