A Cone Property in the Theory of Risk-Sensitive Average Criteria

Abstract

 This work is concerned with finite-state Markov decision chains. It is supposed that the system is driven by a decision-maker assessing a random cost via a utility function \(\ U\). The main objective is to provide explicit examples of utility functions such that, in spite of representing different risk perceptions, (i) render the the same optimal average index, and (ii) share the same average optimal stationary policies. Moreover, it is verified that that family \(\ u\) of utility functions with these two properties form a cone.