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Risk-sensitive average continuous-time Markov decision processes with unbounded transition and cost rates

Part of: Markov processes

Published online by Cambridge University Press:  23 June 2021

Xin Guo  and
Yonghui Huang
Xin Guo*
Affiliation:
Tsinghua University
Yonghui Huang*
Affiliation:
Sun Yat-Sen University
*
*Postal address: School of Economics and Management, Tsinghua University, Beijing, China.
**Postal address: School of Mathematics, Sun Yat-Sen University, and Guangdong Province Key Laboratory of Computational Science, Sun Yat-Sen University, Guangzhou, China. Email address: [email protected]
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Abstract

This paper considers risk-sensitive average optimization for denumerable continuous-time Markov decision processes (CTMDPs), in which the transition and cost rates are allowed to be unbounded, and the policies can be randomized history dependent. We first derive the multiplicative dynamic programming principle and some new facts for risk-sensitive finite-horizon CTMDPs. Then, we establish the existence and uniqueness of a solution to the risk-sensitive average optimality equation (RS-AOE) through the results for risk-sensitive finite-horizon CTMDPs developed here, and also prove the existence of an optimal stationary policy via the RS-AOE. Furthermore, for the case of finite actions available at each state, we construct a sequence of models of finite-state CTMDPs with optimal stationary policies which can be obtained by a policy iteration algorithm in a finite number of iterations, and prove that an average optimal policy for the case of infinitely countable states can be approximated by those of the finite-state models. Finally, we illustrate the conditions and the iteration algorithm with an example.

Keywords

Continuous-time Markov decision processunbounded transition and cost raterisk-sensitive average optimality equationoptimal policyfinite approximation

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 2 , June 2021 , pp. 523 - 550
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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