Geodesic
An optimality system for finite average Markov decision chains under risk-aversion
Kybernetika, Tome 48 (2012) no. 1, pp. 83-104 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Alan{\'\i}s-Dur\'an, Alfredo and Cavazos-Cadena, Rolando},
     title = {An optimality system for finite average {Markov} decision chains under risk-aversion},
     journal = {Kybernetika},
     pages = {83--104},
     year = {2012},
     volume = {48},
     number = {1},
     mrnumber = {2932929},
     zbl = {1243.93127},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_1_a4/}
}
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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/