A Characterization of the Optimal Certainty Equivalent of the Average Cost via the Arrow-Pratt Sensitivity Function

This work is concerned with finite-state irreducible Markov decision chains satisfying continuity-compactness requirements. It is supposed that the system is driven by a decision maker with utility function U , which, aside mild conditions, is arbitrary, and the performance of a control policy is measured by the long-run average cost criterion induced by U . The main conclusions about this performance index are as follows: (i) the optimal U -average value function coincides with the optimal V -average index for a certain exponential utility V , and (ii) the average criteria associated with U and V have the same class of optimal stationary policies.