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

Qingda Wei () and Xian Chen ()
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Qingda Wei: Huaqiao University
Xian Chen: Xiamen University

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 1, No 12, 309-333

Abstract: 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.

Keywords: Continuous-time Markov decision processes; Risk-sensitive first passage discounted cost criterion; Optimal policies; Value iteration.; 90C40; 60J27 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02179-3

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