IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v95y2022i2d10.1007_s00186-022-00779-9.html
   My bibliography  Save this article

Risk-sensitive discounted cost criterion for continuous-time Markov decision processes on a general state space

Author

Listed:
  • Subrata Golui

    (Indian Institute of Technology Guwahati)

  • Chandan Pal

    (Indian Institute of Technology Guwahati)

Abstract

In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates are allowed to be unbounded. Under certain Lyapunov condition, we establish the existence and uniqueness of the solution to the Hamilton–Jacobi–Bellman equation. Also, we prove the existence of optimal risk-sensitive control in the class of Markov control and completely characterized the optimal control.

Suggested Citation

  • Subrata Golui & Chandan Pal, 2022. "Risk-sensitive discounted cost criterion for continuous-time Markov decision processes on a general state space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 219-247, April.
    • Handle: RePEc:spr:mathme:v:95:y:2022:i:2:d:10.1007_s00186-022-00779-9
    DOI: 10.1007/s00186-022-00779-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-022-00779-9
    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/s00186-022-00779-9?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. Qingda Wei, 2016. "Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 461-487, December.
    3. V. Rykov & M. Yu. Kitaev, 1995. "Controlled queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-3, January.
    4. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
    5. Xin Guo & Qiuli Liu & Yi Zhang, 2019. "Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates," 4OR, Springer, vol. 17(4), pages 427-442, December.
    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. Subrata Golui & Chandan Pal & Subhamay Saha, 2022. "Continuous-Time Zero-Sum Games for Markov Decision Processes with Discounted Risk-Sensitive Cost Criterion," Dynamic Games and Applications, Springer, vol. 12(2), pages 485-512, June.
    2. Xin Guo & Qiuli Liu & Yi Zhang, 2019. "Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates," 4OR, Springer, vol. 17(4), pages 427-442, December.
    3. 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.
    4. Wei, Qingda, 2019. "Nonzero-sum risk-sensitive finite-horizon continuous-time stochastic games," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 96-104.
    5. Yonghui Huang & Zhaotong Lian & Xianping Guo, 2022. "Risk-sensitive infinite-horizon discounted piecewise deterministic Markov decision processes," Operational Research, Springer, vol. 22(5), pages 5791-5816, November.
    6. Xianping Guo & Yi Zhang, 2016. "Optimality of Mixed Policies for Average Continuous-Time Markov Decision Processes with Constraints," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1276-1296, November.
    7. 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.
    8. Sebastien Lleo & Wolfgang Runggaldier, 2025. "Exploratory Randomization for Discrete-Time Linear Exponential Quadratic Gaussian (LEQG) Problem," Papers 2501.06275, arXiv.org.
    9. Yi Zhang, 2018. "On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1322-1355, September.
    10. 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.
    11. Dimitri frosinin & L. Breuer, 2006. "Threshold policies for controlled retrial queues with heterogeneous servers," Annals of Operations Research, Springer, vol. 141(1), pages 139-162, January.
    12. 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.
    13. Naci Saldi & Tamer Başar & Maxim Raginsky, 2023. "Partially Observed Discrete-Time Risk-Sensitive Mean Field Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 929-960, September.
    14. Haoyang Cao & Zhengqi Wu & Renyuan Xu, 2024. "Inference of Utilities and Time Preference in Sequential Decision-Making," Papers 2405.15975, arXiv.org, revised Jun 2024.
    15. 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.
    16. Tomasz Kosmala & Randall Martyr & John Moriarty, 2023. "Markov risk mappings and risk-sensitive optimal prediction," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 91-116, February.
    17. Qingda Wei, 2017. "Finite approximation for finite-horizon continuous-time Markov decision processes," 4OR, Springer, vol. 15(1), pages 67-84, March.
    18. Rainer Schlosser, 2016. "Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 153-169, April.
    19. Nicole Bäuerle & Alexander Glauner, 2021. "Minimizing spectral risk measures applied to Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 35-69, August.
    20. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2016. "Uniform ergodicity of continuous-time controlled Markov chains: A survey and new results," Annals of Operations Research, Springer, vol. 241(1), pages 249-293, June.

    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:mathme:v:95:y:2022:i:2:d:10.1007_s00186-022-00779-9. 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.