调整后的高阶预期缺口

IF 1.9 2区经济学 Q2 ECONOMICS Insurance Mathematics & Economics Pub Date : 2024-01-02 DOI:10.1016/j.insmatheco.2023.12.006

Zhenfeng Zou , Taizhong Hu

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引用次数: 0

摘要

如何检测具有相同均值的两个风险随机变量的不同尾部行为是一项重要任务。本文受 Burzoni 等人（2022 年）的启发，引入并研究了一类凸风险度量，即调整后的高阶预期缺口（ES）。调整后的风险度量将风险量化为为确保其高阶 ES 在每个概率水平上不超过预先指定的阈值而必须筹集并注入金融头寸的最低资本量。通过选择风险阈值为特殊基准随机损失的高阶 ES，这一新的风险度量与二元高阶递增凸序密切相关。此外，还给出了（调整后的）高阶预期缺口的对偶表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Adjusted higher-order expected shortfall

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.

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来源期刊

Insurance Mathematics & Economics 管理科学-数学跨学科应用

CiteScore

3.40

自引率

15.80%

发文量

审稿时长

17.3 weeks

期刊介绍： Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.