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Controlled Semi-Markov Chains with Risk-Sensitive Average Cost Criterion

Author

Listed:
  • Selene Chávez-Rodríguez

    (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 semi-Markov decision chains on a finite state space. Assuming that the controller has a constant and positive risk-sensitive coefficient, an optimality equation for the corresponding (long-run) risk-sensitive average cost index is formulated and, under suitable continuity-compactness conditions, it is shown that a solution of such an equation determines the optimal average cost, as well as an optimal stationary policy. Additionally, if the underlying Markov chain is communicating, then it is proved that the optimality equation has a solution.

Suggested Citation

  • Selene Chávez-Rodríguez & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2016. "Controlled Semi-Markov Chains with Risk-Sensitive Average Cost Criterion," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 670-686, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0916-z
    DOI: 10.1007/s10957-016-0916-z
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    References listed on IDEAS

    as
    1. Rolando Cavazos-Cadena & Emmanuel Fernández-Gaucherand, 1999. "Controlled Markov chains with risk-sensitive criteria: Average cost, optimality equations, and optimal solutions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 299-324, April.
    2. 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.
    3. 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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    Cited by:

    1. Bhabak, Arnab & Saha, Subhamay, 2022. "Risk-sensitive semi-Markov decision problems with discounted cost and general utilities," Statistics & Probability Letters, Elsevier, vol. 184(C).
    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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