Reflected BSDEs on filtered probability spaces

Abstract

We study the problem of existence and uniqueness of solutions of backward stochastic differential equations with two reflecting irregular barriers, Lp data and generators satisfying weak integrability conditions. We deal with equations on general filtered probability spaces. In case the generator does not depend on the z variable, we first consider the case p=1 and we only assume that the underlying filtration satisfies the usual conditions of right-continuity and completeness. Additional integrability properties of solutions are established if p∈(1,2] and the filtration is quasi-continuous. In case the generator depends on z, we assume that p=2, the filtration satisfies the usual conditions and additionally that it is separable. Our results apply for instance to Markov-type reflected backward equations driven by general Hunt processes.