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Integro-differential optimality equations for the risk-sensitive control of piecewise deterministic Markov processes

Author

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  • O. L. V. Costa

    (Escola Politécnica da Universidade de São Paulo)

  • F. Dufour

    (Université de Bordeaux)

Abstract

In this paper we study the minimization problem of the infinite-horizon expected exponential utility total cost for continuous-time piecewise deterministic Markov processes with the control acting continuously on the jump intensity $$\lambda $$ λ and on the transition measure Q of the process. The action space is supposed to depend on the state variable and the state space is considered to have a frontier such that the process jumps whenever it touches this boundary. We characterize the optimal value function as the minimal solution of an integro-differential optimality equation satisfying some boundary conditions, as well as the existence of a deterministic stationary optimal policy. These results are obtained by using the so-called policy iteration algorithm, under some continuity and compactness assumptions on the parameters of the problem, as well as some non-explosive conditions for the process.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:2:d:10.1007_s00186-020-00732-8
    DOI: 10.1007/s00186-020-00732-8
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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.
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    Cited by:

    1. 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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