Optimal switching problem and related system of BSDEs with left-Lipschitz coefficients and mixed reflections

This paper studies a system of backward stochastic differential equations with both oblique and normal reflections which arises in the study of the optimal switching problem. The main feature of our system is that its components are interconnected through both the obstacles and the generators which are only assumed to be left-Lipschitz continuous with respect to y. We provide an existence theorem of minimal solutions for RBSDEs in this framework.