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Almost first-order stochastic dominance by distorted expectations

Part of: Distribution theory - Probability Mathematical economics

Published online by Cambridge University Press:  12 August 2022

Jianping Yang ,
Tian Zhou  and
Weiwei Zhuang Open the ORCID record for Weiwei Zhuang [Opens in a new window]
Jianping Yang
Affiliation:
Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China. E-mails: yangjp@zstu.edu.cn; ztian980117@163.com
Tian Zhou
Affiliation:
Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China. E-mails: yangjp@zstu.edu.cn; ztian980117@163.com
Weiwei Zhuang
Affiliation:
International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China. E-mail: weizh@ustc.edu.cn
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Abstract

Almost stochastic dominance has been receiving a great amount of attention in the financial and economic literatures. In this paper, we characterize the properties of almost first-order stochastic dominance (AFSD) via distorted expectations and investigate the conditions under which AFSD is preserved under a distortion transform. The main results are also applied to establish stochastic comparisons of order statistics and receiver operating characteristic curves via AFSD.

Keywords

Almost first-order stochastic dominanceDecision analysisDistortion functionOrder statisticsROC curve

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 91B16: Utility theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 4 , October 2023 , pp. 888 - 906
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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