IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v184y2022ics0167715222000281.html
   My bibliography  Save this article

Risk-sensitive semi-Markov decision problems with discounted cost and general utilities

Author

Listed:
  • Bhabak, Arnab
  • Saha, Subhamay

Abstract

In this article we consider risk-sensitive control of semi-Markov processes with a discrete state space. We consider general utility functions and discounted cost in the optimization criteria. We consider random finite horizon and infinite horizon problems. Using a state augmentation technique we characterize the value functions and also prescribe optimal controls.

Suggested Citation

  • Bhabak, Arnab & Saha, Subhamay, 2022. "Risk-sensitive semi-Markov decision problems with discounted cost and general utilities," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000281
    DOI: 10.1016/j.spl.2022.109408
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222000281
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109408?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. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    2. Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.
    3. 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.
    4. Arapostathis, Ari & Biswas, Anup, 2018. "Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1485-1524.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Ghosh, Mrinal K. & Golui, Subrata & Pal, Chandan & Pradhan, Somnath, 2023. "Discrete-time zero-sum games for Markov chains with risk-sensitive average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 40-74.
    2. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    3. Nicole Bäuerle & Anna Jaśkiewicz, 2024. "Markov decision processes with risk-sensitive criteria: an overview," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(1), pages 141-178, April.
    4. 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.
    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. 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.
    7. 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.
    8. Rubén Blancas-Rivera & Rolando Cavazos-Cadena & Hugo Cruz-Suárez, 2020. "Discounted approximations in risk-sensitive average Markov cost chains with finite state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 241-268, April.
    9. Arnab Basu & Tirthankar Bhattacharyya & Vivek S. Borkar, 2008. "A Learning Algorithm for Risk-Sensitive Cost," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 880-898, November.
    10. Brias, Antoine & Munch, Stephan B., 2021. "Ecosystem based multi-species management using Empirical Dynamic Programming," Ecological Modelling, Elsevier, vol. 441(C).
    11. Qingda Wei & Xian Chen, 2023. "Continuous-Time Markov Decision Processes Under the Risk-Sensitive First Passage Discounted Cost Criterion," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 309-333, April.
    12. Sebastien Lleo & Wolfgang Runggaldier, 2025. "Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem," Papers 2501.06275, arXiv.org.
    13. O. L. V. Costa & F. Dufour, 2021. "Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 327-357, April.
    14. 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.
    15. Tomasz R. Bielecki & Igor Cialenco & Andrzej Ruszczy'nski, 2022. "Risk Filtering and Risk-Averse Control of Markovian Systems Subject to Model Uncertainty," Papers 2206.09235, arXiv.org.
    16. Guglielmo D’Amico & Fulvio Gismondi & Jacques Janssen & Raimondo Manca, 2015. "Discrete Time Homogeneous Markov Processes for the Study of the Basic Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 983-998, December.
    17. Constantin Waubert de Puiseau & Richard Meyes & Tobias Meisen, 2022. "On reliability of reinforcement learning based production scheduling systems: a comparative survey," Journal of Intelligent Manufacturing, Springer, vol. 33(4), pages 911-927, April.
    18. Bäuerle, Nicole & Jaśkiewicz, Anna, 2017. "Optimal dividend payout model with risk sensitive preferences," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 82-93.
    19. Jelito, Damian & Pitera, Marcin & Stettner, Łukasz, 2021. "Risk sensitive optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 125-144.
    20. Qingda Wei & Xian Chen, 2021. "Nonzero-sum Risk-Sensitive Average Stochastic Games: The Case of Unbounded Costs," Dynamic Games and Applications, Springer, vol. 11(4), pages 835-862, December.

    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:eee:stapro:v:184:y:2022:i:c:s0167715222000281. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.