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Adjusted higher-order expected shortfall

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  • Zou, Zhenfeng
  • Hu, Taizhong

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.

Suggested Citation

  • Zou, Zhenfeng & Hu, Taizhong, 2024. "Adjusted higher-order expected shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 1-12.
    • Handle: RePEc:eee:insuma:v:115:y:2024:i:c:p:1-12
    DOI: 10.1016/j.insmatheco.2023.12.006
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    More about this item

    Keywords

    Convex risk measure; Coherent risk measure; Higher-order expected shortfall; Risk profile; Dual increasing convex order; Dual representation;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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