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.