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Risk-Sensitive Markov Decision Processes

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Author Info

  • Ronald A. Howard

    (Stanford University)

  • James E. Matheson

    (Stanford Research Institute)

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    Abstract

    This paper considers the maximization of certain equivalent reward generated by a Markov decision process with constant risk sensitivity. First, value iteration is used to optimize possibly time-varying processes of finite duration. Then a policy iteration procedure is developed to find the stationary policy with highest certain equivalent gain for the infinite duration case. A simple example demonstrates both procedures.

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    File URL: http://dx.doi.org/10.1287/mnsc.18.7.356
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 18 (1972)
    Issue (Month): 7 (March)
    Pages: 356-369

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    Handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:356-369

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    Cited by:
    1. Hałaj, Grzegorz & Kok, Christoffer, 2014. "Modeling emergence of the interbank networks," Working Paper Series 1646, European Central Bank.
    2. 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.
    3. Kang Boda & Jerzy Filar, 2006. "Time Consistent Dynamic Risk Measures," Computational Statistics, Springer, vol. 63(1), pages 169-186, February.
    4. Muller, Alfred, 2000. "Expected utility maximization of optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 122(1), pages 101-114, April.
    5. Dellaert, N.P. & Frenk, J.B.G. & van Rijsoort, L.P., 1993. "Optimal claim behaviour for vehicle damage insurances," Econometric Institute Research Papers 11669, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Pestien, Victor & Wang, Xiaobo, 1998. "Markov-achievable payoffs for finite-horizon decision models," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 101-118, January.
    7. Basu, Arnab & Ghosh, Mrinal Kanti, 2014. "Zero-sum risk-sensitive stochastic games on a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 961-983.
    8. Nicole Bäuerle & Jonathan Ott, 2011. "Markov Decision Processes with Average-Value-at-Risk criteria," Computational Statistics, Springer, vol. 74(3), pages 361-379, December.
    9. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    10. Rolando Cavazos-Cadena, 2009. "Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria," Computational Statistics, Springer, vol. 70(3), pages 541-566, December.
    11. C. Barz & K. Waldmann, 2007. "Risk-sensitive capacity control in revenue management," Computational Statistics, Springer, vol. 65(3), pages 565-579, June.
    12. Monahan, George E. & Sobel, Matthew J., 1997. "Risk-Sensitive Dynamic Market Share Attraction Games," Games and Economic Behavior, Elsevier, vol. 20(2), pages 149-160, August.
    13. Rolando Cavazos-Cadena, 2010. "Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains," Computational Statistics, Springer, vol. 71(1), pages 47-84, February.

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