Discounted Approximations for Risk‐Sensitive Average Criteria in Markov Decision Chains with Finite State Space

This work concerns Markov decision processes with finite state space and compact action set. The performance of a control policy is measured by a risk‐sensitive average cost criterion and, under standard continuity‐compactness conditions, it is shown that the discounted approximations converge to the optimal value function, and that the superior and inferior limit average criteria have the same optimal value function. These conclusions are obtained for every nonnull risk‐sensitivity coefficient, and regardless of the communication structure induced by the transition law.