Solution to the risk-sensitive average optimality equation in communicating Markov decision chains with finite state space: An alternative approach (Q1812296)

This paper studies Markov decision chains with finite state and action-sets. The decision maker is assumed to be risk averse with constant risk sensitive coefficient \(\lambda\) and the performance of a control policy is measured by the risk-sensitive average cost criterion. Using a contractive operator and the vanishing discount approach, the authors present an alternative proof for the existence result [\textit{R. A. Howard} and \textit{J. E. Matheson}, Manage. Sci., Theory 18, 356--369 (1972; Zbl 0238.90007)], which says that the optimality equation has a solution for every \(\lambda> 0\), when the whole state space is a communication class under the action of each stationary policy.