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Risk-Sensitive and Mean Variance Optimality in Markov Decision Processes

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  • Karel Sladký

    ()
    (Academy of Sciences of the Czech Republic, Institute of Information Theory and Automation, Department of Econometrics, Prague, Czech Republic)

Abstract

In this paper we consider unichain Markov decision processes with finite state space and compact actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivity coefficient (so-called risk-sensitive models). If the risk sensitivity coefficient equals zero (risk-neutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risk-sensitive case we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent, that take into account not only the expected values of the total reward but also its higher moments.

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Bibliographic Info

Article provided by Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies in its journal Czech Economic Review.

Volume (Year): 7 (2013)
Issue (Month): 3 (November)
Pages: 146-161

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Handle: RePEc:fau:aucocz:au2013_146

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Related research

Keywords: Discrete-time Markov decision chains; exponential utility functions; certainty equivalent; mean-variance optimality; connections between risk-sensitive and risk-neutral models;

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  1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  2. Kawai, Hajime, 1987. "A variance minimization problem for a Markov decision process," European Journal of Operational Research, Elsevier, vol. 31(1), pages 140-145, July.
  3. Stratton C. Jaquette, 1976. "A Utility Criterion for Markov Decision Processes," Management Science, INFORMS, vol. 23(1), pages 43-49, September.
  4. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
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