Systems of BSDES with oblique reflection and related optimal switching problems

Abstract

We consider systems of backward stochastic differential equations with càdlàg 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 quasimonotone generators. Applications to the optimal switching problem are given. MSC: Primary 60H10; Secondary 60H30, 91B70.