Zero-Sum Stochastic Differential Games 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.