Risk-sensitive infinite-horizon discounted piecewise deterministic Markov decision processes

Yonghui Huang (), Zhaotong Lian () and Xianping Guo ()
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Yonghui Huang: Sun Yat-Sen University
Zhaotong Lian: Faculty of Business Administration, University of Macau
Xianping Guo: Sun Yat-Sen University

Operational Research, 2022, vol. 22, issue 5, No 35, 5816 pages

Abstract: Abstract This paper deals with risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of an infinite-horizon discounted cost is minimized. Both the transition rate and cost rate are allowed to be unbounded. Based on a dynamic programming observation, we introduce an auxiliary function with the time as an additional variable to analyze the problem, which is different from those with the risk-sensitive parameter as an additional variable in previous works. Under suitable assumptions, we derive the associated Feynman-Kac’s formula, and then establish the associated Hamilton–Jacobi–Bellman equation with the time as a differential variable, which leads to the existence of optimal policies depending on the time, explicitly showing that the risk-sensitive discounted optimal policies are not stationary.

Keywords: Piecewise deterministic Markov decision processes; Risk sensitive; Discounted cost; HJB equation; Non-stationarity; 90C40; 93E20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s12351-022-00726-w

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