Optimal switching, systems of reflected BSDEs and systems of variational inequalities with inter-connected obstacles

Abstract

This paper deals with the optimal switching problem with multiple regimes. We first provide a Verification Theorem, expressed by Snell envelope of processes, and later we show that it has a solution. We then study the connection with systems of reflected BSDEs with oblique reflection. In the case when randomness stems from a diffusion process, we study the relation of the problem with systems of variational inequalities with inter-connected obstacles. We prove that this latter has a unique continuous solution in viscosity sense.