期望缺额对偶表示的初步证明

IF 0.9 3区经济学 Q3 BUSINESS, FINANCE

Mathematics and Financial Economics Pub Date : 2023-11-16 DOI:10.1007/s11579-023-00346-8

Martin Herdegen, Cosimo Munari

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引用次数: 0

摘要

给出了一般概率空间上可积随机变量空间上期望不足的对偶表示的一个初等证明。与现有文献的结果不同，我们的证明只利用了分位数函数的基本性质，因此可以很容易地在任何研究生课程中实施风险措施。作为副产品，我们得到了期望缺额的子可加性的一个新证明。

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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An elementary proof of the dual representation of Expected Shortfall

We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic properties of quantile functions and can thus be easily implemented in any graduate course on risk measures. As a byproduct, we obtain a new proof of the subadditivity of Expected Shortfall.

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来源期刊

Mathematics and Financial Economics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS -

CiteScore

2.80

自引率

6.20%

发文量

期刊介绍： The primary objective of the journal is to provide a forum for work in finance which expresses economic ideas using formal mathematical reasoning. The work should have real economic content and the mathematical reasoning should be new and correct.