Geodesic
An optimality system for finite average Markov decision chains under risk-aversion
Kybernetika, Tome 48 (2012) no. 1, pp. 83-104.

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This work concerns controlled Markov chains with finite state space and compact action sets. The decision maker is risk-averse with constant risk-sensitivity, and the performance of a control policy is measured by the long-run average cost criterion. Under standard continuity-compactness conditions, it is shown that the (possibly non-constant) optimal value function is characterized by a system of optimality equations which allows to obtain an optimal stationary policy. Also, it is shown that the optimal superior and inferior limit average cost functions coincide.
Classification : 60J05, 93C55, 93E20
Keywords: partition of the state space; nonconstant optimal average cost; discounted approximations to the risk-sensitive average cost criterion; equality of superior and inferior limit risk-averse average criteria 
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     title = {An optimality system for finite average {Markov} decision chains under risk-aversion},
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Alanís-Durán, Alfredo; Cavazos-Cadena, Rolando. An optimality system for finite average Markov decision chains under risk-aversion. Kybernetika, Tome 48 (2012) no. 1, pp. 83-104. http://geodesic.mathdoc.fr/item/KYB_2012__48_1_a4/