Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion

Qingda Wei ()
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Qingda Wei: Huaqiao University

Mathematical Methods of Operations Research, 2016, vol. 84, issue 3, No 2, 487 pages

Abstract: Abstract This paper studies continuous-time Markov decision processes with a denumerable state space, a Borel action space, bounded cost rates and possibly unbounded transition rates under the risk-sensitive finite-horizon cost criterion. We give the suitable optimality conditions and establish the Feynman–Kac formula, via which the existence and uniqueness of the solution to the optimality equation and the existence of an optimal deterministic Markov policy are obtained. Moreover, employing a technique of the finite approximation and the optimality equation, we present an iteration method to compute approximately the optimal value and an optimal policy, and also give the corresponding error estimations. Finally, a controlled birth and death system is used to illustrate the main results.

Keywords: Continuous-time Markov decision processes; Risk-sensitive finite-horizon cost criterion; Unbounded transition rates; Feynman–Kac formula; Finite approximation; 93E20; 90C40 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00186-016-0550-4

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