Systems of BSDES with oblique reflection and related optimal switching problems

We consider systems of backward stochastic differential equations with cadlag upper barrier U and oblique reflection from below driven by an increasing continuous function H. Our equations are defined on general probability spaces with a filtration satisfying merely the usual assumptions of right continuity and completeness. We assume that the pair (H(U), U) satisfies a Mokobodzki-type condition. We prove the existence of a solution for integrable terminal conditions and integrable quasi-monotone generators. Applications to the optimal switching problem are given.