On the equality of solutions of max–min and min–max systems of variational inequalities with interconnected bilateral obstacles

摘要

Abstract In this paper, we deal with the solutions of systems of PDEs with bilateral interconnected obstacles of min–max and max–min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min–max and max–min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the values of a zero-sum switching game is studied. ]]>