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A Discounted Approach in Communicating Average Markov Decision Chains Under Risk-Aversion

Author

Listed:
  • Julio Saucedo-Zul

    (Benemérita Universidad Autónoma de Puebla)

  • Rolando Cavazos-Cadena

    (Universidad Autónoma Agraria Antonio Narro)

  • Hugo Cruz-Suárez

    (Benemérita Universidad Autónoma de Puebla)

Abstract

This work concerns with discrete-time Markov decision processes on a denumerable state space. Assuming that the decision maker is risk-averse with constant risk-sensitivity coefficient, the performance of a control policy is measured by an average criterion associated with a non-negative and bounded cost function. Under conditions ensuring that the optimal average cost is constant, but not necessarily determined via the average cost optimality equation, it is shown that a discounted criterion can be used to approximate the optimal average index.

Suggested Citation

  • Julio Saucedo-Zul & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2020. "A Discounted Approach in Communicating Average Markov Decision Chains Under Risk-Aversion," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 585-606, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01758-y
    DOI: 10.1007/s10957-020-01758-y
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    References listed on IDEAS

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    5. 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.
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    8. Marcin Pitera & Łukasz Stettner, 2016. "Long run risk sensitive portfolio with general factors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 265-293, April.
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    Cited by:

    1. Gustavo Portillo-Ramírez & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2023. "Contractive approximations in average Markov decision chains driven by a risk-seeking controller," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 75-91, August.
    2. Carlos Camilo-Garay & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2022. "Contractive Approximations in Risk-Sensitive Average Semi-Markov Decision Chains on a Finite State Space," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 271-291, January.

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