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Risk-sensitive semi-Markov decision processes with general utilities and multiple criteria

Part of: Stochastic systems and control

Published online by Cambridge University Press:  16 November 2018

Yonghui Huang ,
Zhaotong Lian  and
Xianping Guo
Yonghui Huang*
Affiliation:
Sun Yat-Sen University
Zhaotong Lian*
Affiliation:
University of Macau
Xianping Guo*
Affiliation:
Sun Yat-Sen University
*
* Postal address: School of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China.
*** Postal address: Faculty of Business Administration, University of Macau, Macau, China. Email address: lianzt@umac.mo
* Postal address: School of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China.
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Abstract

In this paper we investigate risk-sensitive semi-Markov decision processes with a Borel state space, unbounded cost rates, and general utility functions. The performance criteria are several expected utilities of the total cost in a finite horizon. Our analysis is based on a type of finite-horizon occupation measure. We express the distribution of the finite-horizon cost in terms of the occupation measure for each policy, wherein the discount is not needed. For unconstrained and constrained problems, we establish the existence and computation of optimal policies. In particular, we develop a linear program and its dual program for the constrained problem and, moreover, establish the strong duality between the two programs. Finally, we provide two special cases of our results, one of which concerns the discrete-time model, and the other the chance-constrained problem.

Keywords

Semi-Markov decision processfinite-horizon costoccupation measureexpected utilitylinear program

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 93E20: Optimal stochastic control
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 3 , September 2018 , pp. 783 - 804
Copyright
Copyright © Applied Probability Trust 2018 

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