Worst-case distortion riskmetrics and weighted entropy with partial information

Baishuai Zuo and Chuancun Yin

European Journal of Operational Research, 2025, vol. 321, issue 2, 476-492

Abstract: In this paper, we discuss the worst-case distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to a general class of distortion risk measures and variability measures. Furthermore, we also consider the worst-case weighted entropy for general distributions when only partial information is available. Specifically, we provide some applications for entropies, weighted entropies and risk measures. The commonly used entropies include Gini functional, cumulative residual entropy, tail-Gini functional, cumulative Tsallis past entropy, extended Gini coefficient, among others. The risk measures contain some premium principles and shortfalls based on entropy. The shortfalls include the Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy and shortfall of cumulative residual Tsallis entropy with order α.

Keywords: Distortion riskmetrics; Premium principles; Shortfalls; Weighted entropy; Worst-case (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:321:y:2025:i:2:p:476-492

DOI: 10.1016/j.ejor.2024.09.047

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