Abstract.
This note concerns Markov decision chains with finite state and action sets. The decision maker is assumed to be risk-averse with constant risk sensitive coefficient λ, and the performance of a control policy is measured by the risk-sensitive average cost criterion. In their seminal paper Howard and Matheson established that, when the whole state space is a communicating class under the action of each stationary policy, then there exists a solution to the optimality equation for every λ>0. This paper presents an alternative proof of this fundamental result, which explicitly highlights the essential role of the communication properties in the analysis of the risk-sensitive average cost criterion.
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Manuscript received: November 2001/Final version received: April 2002
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ID="*" This work was supported by the PSF Organization under Grant No. 010/300/01-4 and Conacyt Grant 37643-E
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Cavazos-Cadena, R., Hernández-Hernández, D. Solution to the risk-sensitive average optimality equation in communicating Markov decision chains with finite state space: An alternative approach. Mathematical Methods of OR 56, 473–479 (2003). https://doi.org/10.1007/s001860200229
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DOI: https://doi.org/10.1007/s001860200229