IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v170y2016i2d10.1007_s10957-016-0916-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0916-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-016-0916-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. V. S. Borkar & S. P. Meyn, 2002. "Risk-Sensitive Optimal Control for Markov Decision Processes with Monotone Cost," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 192-209, February.
    4. 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.
    5. Rolando Cavazos-Cadena, 2018. "Characterization of the Optimal Risk-Sensitive Average Cost in Denumerable Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 1025-1050, August.
    6. Daniel Hernández Hernández & Diego Hernández Bustos, 2017. "Local Poisson Equations Associated with Discrete-Time Markov Control Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 1-29, April.
    7. Özlem Çavuş & Andrzej Ruszczyński, 2014. "Computational Methods for Risk-Averse Undiscounted Transient Markov Models," Operations Research, INFORMS, vol. 62(2), pages 401-417, April.
    8. Rolando Cavazos-Cadena & Raúl Montes-de-Oca, 2003. "The Value Iteration Algorithm in Risk-Sensitive Average Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 752-776, November.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Rolando Cavazos-Cadena & Daniel Hernández-Hernández, 2011. "Discounted Approximations for Risk-Sensitive Average Criteria in Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 133-146, February.
    15. 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.
    16. Arnab Basu & Mrinal K. Ghosh, 2018. "Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 516-532, May.
    17. Zeynep Erkin & Matthew D. Bailey & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2010. "Eliciting Patients' Revealed Preferences: An Inverse Markov Decision Process Approach," Decision Analysis, INFORMS, vol. 7(4), pages 358-365, December.
    18. 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.
    19. Erick Delage & Shie Mannor, 2010. "Percentile Optimization for Markov Decision Processes with Parameter Uncertainty," Operations Research, INFORMS, vol. 58(1), pages 203-213, February.
    20. Naci Saldi & Tamer Bas¸ ar & Maxim Raginsky, 2020. "Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1596-1620, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0916-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.