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On approximations of value at risk and expected shortfall involving kurtosis
Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2021-01-17 , DOI: 10.1080/03610918.2020.1869985
Mátyás Barczy 1 , Ádám Dudás 2 , József Gáll 3
Affiliation  

Abstract

We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our approximations are motivated by that kind of extensions of the so-called Normal Power Approximation, used for approximating the cumulative distribution function of a random variable, which incorporate not only the skewness but the kurtosis of the random variable in question as well. We show the performance of our approximations in numerical examples and we also give comparisons with some known ones in the literature.



中文翻译:

关于涉及峰态的风险价值和预期短缺的近似值

摘要

我们推导出具有正偏度和超峰度的高水平损失分布的风险价值和预期短缺的新近似值,并且我们描述了它们对显着分布(例如指数分布、帕累托 I 型分布、对数正态分布和复合(泊松)分布)的精确度. 我们的近似是由所谓的正态功率近似的那种扩展驱动的,用于近似随机变量的累积分布函数,它不仅包含偏度,还包含所讨论的随机变量的峰度。我们在数值示例中展示了我们的近似值的性能,我们还与文献中的一些已知的进行了比较。

更新日期:2021-01-17
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