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Risk-Sensitive and Mean Variance Optimality in Markov Decision Processes


  • Karel Sladký

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


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.

Suggested Citation

  • Karel Sladký, 2013. "Risk-Sensitive and Mean Variance Optimality in Markov Decision Processes," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(3), pages 146-161, November.
  • Handle: RePEc:fau:aucocz:au2013_146

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    References listed on IDEAS

    1. Stratton C. Jaquette, 1976. "A Utility Criterion for Markov Decision Processes," Management Science, INFORMS, vol. 23(1), pages 43-49, September.
    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. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    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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    More about this item


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

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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