The Annals of Applied Probability

A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains

Rolando Cavazos-Cadena and Daniel Hernández-Hernández

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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.

Article information

Ann. Appl. Probab. Volume 15, Number 1A (2005), 175-212.

First available: 28 January 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control 60F10: Large deviations
Secondary: 93C55: Discrete-time systems

Decreasing function along trajectories stopping time nearly optimal policies Hölder’s inequality simultaneous Doeblin condition recurrent state


Cavazos-Cadena, Rolando; Hernández-Hernández, Daniel. A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains. The Annals of Applied Probability 15 (2005), no. 1A, 175--212. doi:10.1214/105051604000000585.

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