Adjusted higher-order expected shortfall

Zhenfeng Zou and Taizhong Hu

Insurance: Mathematics and Economics, 2024, vol. 115, issue C, 1-12

Abstract: How to detect different tail behaviors of two risk random variables with the same mean is an important task. In this paper, motivated by Burzoni et al. (2022), a class of convex risk measures, referred to as adjusted higher-order Expected Shortfall (ES), is introduced and studied. The adjusted risk measure quantifies risk as the minimum amount of capital that has to be raised and injected into a financial position to ensure that its higher-order ES does not exceed a pre-specified threshold for every probability level. This new risk measure is intimately linked to dual higher-order increasing convex order by choosing the risk threshold to be the higher-order ES of a special benchmark random loss. The dual representation for (adjusted) higher-order Expected Shortfall is also given.

Keywords: Convex risk measure; Coherent risk measure; Higher-order expected shortfall; Risk profile; Dual increasing convex order; Dual representation (search for similar items in EconPapers)
JEL-codes: D81 G22 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:115:y:2024:i:c:p:1-12

DOI: 10.1016/j.insmatheco.2023.12.006

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