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Aging notions, stochastic orders, and expected utilities

Part of: Operations research and management science Distribution theory - Probability Mathematical economics

Published online by Cambridge University Press:  18 October 2023

Jianping Yang ,
Weiwei Zhuang  and
Taizhong Hu Open the ORCID record for Taizhong Hu [Opens in a new window]
Jianping Yang*
Affiliation:
University of Science and Technology of China, Zhejiang Sci-Tech University
Weiwei Zhuang*
Affiliation:
University of Science and Technology of China
Taizhong Hu*
Affiliation:
University of Science and Technology of China
*
*Postal address: Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
*Postal address: Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
*Postal address: Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
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Abstract

There are some connections between aging notions, stochastic orders, and expected utilities. It is known that the DRHR (decreasing reversed hazard rate) aging notion can be characterized via the comparative statics result of risk aversion, and that the location-independent riskier order preserves monotonicity between risk premium and the Arrow–Pratt measure of risk aversion, and that the dispersive order preserves this monotonicity for the larger class of increasing utilities. Here, the aging notions ILR (increasing likelihood ratio), IFR (increasing failure rate), IGLR (increasing generalized likelihood ratio), and IGFR (increasing generalized failure rate) are characterized in terms of expected utilities. Based on these observations, we recover the closure properties of ILR, IFR, and DRHR under convolution, and of IGLR and IGFR under product, and investigate the closure properties of the dispersive order, location-independent riskier order, excess wealth order, the total time on test transform order under convolution, and the star order under product. We have some new findings.

Keywords

Stochastic comparisonsrisk aversionincreasing likelihood ratioincreasing failure ratedecreasing reversed hazard rateincreasing generalized likelihood ratioincreasing generalized failure rate

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91B16: Utility theory 90B25: Reliability, availability, maintenance, inspection
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 14
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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