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Risk-Sensitive Markov Decision Processes

Author

Listed:
  • Ronald A. Howard

    (Stanford University)

  • James E. Matheson

    (Stanford Research Institute)

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.

Suggested Citation

  • Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
  • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:356-369
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    File URL: http://dx.doi.org/10.1287/mnsc.18.7.356
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    Citations

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    Cited by:

    1. Rolando Cavazos-Cadena, 2010. "Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 47-84, February.
    2. Nicole Bäuerle & Jonathan Ott, 2011. "Markov Decision Processes with Average-Value-at-Risk criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 361-379, December.
    3. C. Barz & K. Waldmann, 2007. "Risk-sensitive capacity control in revenue management," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 565-579, June.
    4. 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.
    5. 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.
    6. Selene Chávez-Rodríguez & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2015. "Continuity of the optimal average cost in Markov decision chains with small risk-sensitivity," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 269-298, June.
    7. Takayuki Osogami, 2012. "Iterated risk measures for risk-sensitive Markov decision processes with discounted cost," Papers 1202.3755, arXiv.org.
    8. Rolando Cavazos-Cadena, 2009. "Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 541-566, December.
    9. repec:spr:compst:v:74:y:2011:i:3:p:361-379 is not listed on IDEAS
    10. repec:spr:compst:v:71:y:2010:i:1:p:47-84 is not listed on IDEAS
    11. Grzegorz Hałaj, 2016. "Dynamic Balance Sheet Model With Liquidity Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-37, November.
    12. repec:spr:compst:v:70:y:2009:i:3:p:541-566 is not listed on IDEAS
    13. Muller, Alfred, 2000. "Expected utility maximization of optimal stopping problems," European Journal of Operational Research, Elsevier, vol. 122(1), pages 101-114, April.
    14. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    15. 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.
    16. repec:spr:joptap:v:173:y:2017:i:1:d:10.1007_s10957-017-1076-5 is not listed on IDEAS
    17. 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.
    18. 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.
    19. repec:spr:compst:v:65:y:2007:i:3:p:565-579 is not listed on IDEAS
    20. Kok, Christoffer & Hałaj, Grzegorz, 2014. "Modeling emergence of the interbank networks," Working Paper Series 1646, European Central Bank.
    21. repec:spr:compst:v:63:y:2006:i:1:p:169-186 is not listed on IDEAS
    22. repec:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0916-z is not listed on IDEAS
    23. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    24. Kang Boda & Jerzy Filar, 2006. "Time Consistent Dynamic Risk Measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 169-186, February.

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