We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the existence and uniqueness of the solution to the optimality equation out of a class of possibly unbounded functions, to which the Feynman–Kac formula was also justified to hold.
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This work is partially supported by Natural Science Foundation of Guangdong Province (Grant No. 2014A030313438), Zhujiang New Star (Grant No. 201506010056), Guangdong Province outstanding young teacher training plan (Grant No. YQ2015050).
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Guo, X., Liu, Q. & Zhang, Y. Finite horizon risk-sensitive continuous-time Markov decision processes with unbounded transition and cost rates. 4OR-Q J Oper Res 17, 427–442 (2019). https://doi.org/10.1007/s10288-019-0398-6
- Continuous-time Markov decision processes
- Risk-sensitive criterion
- Optimality equation
Mathematics Subject Classification
- Primary 90C40
- Secondary 60J75