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Risk-sensitive infinite-horizon discounted piecewise deterministic Markov decision processes

Author

Listed:
  • Yonghui Huang

    (Sun Yat-Sen University)

  • Zhaotong Lian

    (Faculty of Business Administration, University of Macau)

  • Xianping Guo

    (Sun Yat-Sen University)

Abstract

This paper deals with risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of an infinite-horizon discounted cost is minimized. Both the transition rate and cost rate are allowed to be unbounded. Based on a dynamic programming observation, we introduce an auxiliary function with the time as an additional variable to analyze the problem, which is different from those with the risk-sensitive parameter as an additional variable in previous works. Under suitable assumptions, we derive the associated Feynman-Kac’s formula, and then establish the associated Hamilton–Jacobi–Bellman equation with the time as a differential variable, which leads to the existence of optimal policies depending on the time, explicitly showing that the risk-sensitive discounted optimal policies are not stationary.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00726-w
    DOI: 10.1007/s12351-022-00726-w
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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. 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.
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