A Characterization of the optimal risk-Sensitive average cost in finite controlled Markov chains

Details A Characterization of the optimal risk-Sensitive average cost in finite controlled Markov chains A Characterization of the optimal risk-Sensitive average cost in finite controlled Markov chains

2005-03-23

arxiv.org/abs/math/0503478v1

Annals of Applied Probability 2005, Vol. 15, No. 1A, 175-212

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000585 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000585

This work concerns controlled Markov chains with finite state and action spaces. The transition law satisfies the simultaneous Doeblin condition, and the performance of a control policy is measured by the (long-run) risk-sensitive average cost criterion associated to a positive, but otherwise arbitrary, risk sensitivity coefficient. Within this context, the optimal risk-sensitive average cost is characterized via a minimization problem in a finite-dimensional Euclidean space.

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