Cavazos-cadena, Rolando et Hernández-hernández, Daniel, A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains, Annals of applied probability , 15((1A)), 2005, pp. 175-212
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.