Zero-sum stochastic differential game with risk-sensitive cost

Abstract: Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize all possible saddle point strategies in the class of stationary Markov controls. In addition, we also establish existence-uniqueness result for the value function of the Hamilton-Jacobi-Isaacs equation.