Average criteria in denumerable semi-Markov decision chains under risk-aversion

This note concerns with semi-Markov decision chains evolving on a denumerable state space. The system is directed by a risk-averse controller with constant risk-sensitivity, and the performance of a decision policy is measured by a long-run average criterion associated with bounded holding cost rates and one-step cost function. Under mild conditions on the sojourn times and the transition law, restrictions on the cost structure are given to ensure that the optimal average cost can be characterized via a bounded solution of the optimality equation. Such a result is used to establish a general characterization of the optimal average cost in terms of an optimality inequality from which an optimal stationary policy can be derived.