Solution to the risk-sensitive average optimality equation in communicating Markov decision chains with finite state space: An alternative approach

Rolando Cavazos-Cadena and Daniel Hernández-Hernández

Mathematical Methods of Operations Research, 2003, vol. 56, issue 3, 473-479

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. Copyright Springer-Verlag Berlin Heidelberg 2003

Keywords: AMS Subject Classification: 93E20; 93B36; Key words: Contractive operator; Vanishing discount approach; Risk sensitive control (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s001860200229

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