Continuous-Time Zero-Sum Games for Markov Decision Processes with Discounted Risk-Sensitive Cost Criterion

In this paper, we study two-person zero-sum stochastic games for controlled continuous time Markov decision processes with risk-sensitive discounted cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum stochastic game, we prove the existence of the value of the game and saddle-point equilibrium in the class of history dependent strategies under a Foster–Lyapunov condition. We achieve our results by studying the corresponding Hamilton–Jacobi–Isaacs equation.