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Continuous-Time Markov Decision Processes Under the Risk-Sensitive First Passage Discounted Cost Criterion

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  • Qingda Wei

    (Huaqiao University)

  • Xian Chen

    (Xiamen University)

Abstract

This paper studies the risk-sensitive first passage discounted cost criterion for continuous-time Markov decision processes with the Borel state and action spaces. The cost and transition rates are allowed to be unbounded. We introduce a new value iteration to establish the existence of a solution to the risk-sensitive first passage discounted cost optimality equation. Then applying the Feynman–Kac formula, we show that the risk-sensitive first passage discounted cost optimal value function is a unique solution to the risk-sensitive first passage discounted cost optimality equation. Moreover, we derive the existence of a deterministic Markov optimal policy in the class of randomized history-dependent policies. Finally, a cash flow model is given to illustrate the results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:1:d:10.1007_s10957-023-02179-3
    DOI: 10.1007/s10957-023-02179-3
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    References listed on IDEAS

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    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. 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. 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.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    5. 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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