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Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates

Author

Listed:
  • Xin Guo

    (University of Liverpool)

  • Qiuli Liu

    (South China Normal University)

  • Yi Zhang

    (University of Liverpool)

Abstract

We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the existence and uniqueness of the solution to the optimality equation out of a class of possibly unbounded functions, to which the Feynman–Kac formula was also justified to hold.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aqjoor:v:17:y:2019:i:4:d:10.1007_s10288-019-0398-6
    DOI: 10.1007/s10288-019-0398-6
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    References listed on IDEAS

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    1. 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.
    2. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
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    4. Rolando Cavazos-Cadena & Raúl Montes-de-Oca, 2000. "Nearly optimal policies in risk-sensitive positive dynamic programming on discrete spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 133-167, September.
    5. V. Rykov & M. Yu. Kitaev, 1995. "Controlled queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-3, January.
    6. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.

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