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

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  • 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
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    References listed on IDEAS

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    3. 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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    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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