英文标题：
《On approximations of Value at Risk and Expected Shortfall involving
  kurtosis》
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作者：
Matyas Barczy, Adam Dudas, Jozsef Gall
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最新提交年份：
2020
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英文摘要：
  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.
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中文摘要：
我们推导了具有正偏度和超额峰度的高水平损失分布的风险值和预期短缺的新近似值，并描述了它们对于指数、帕累托I型、对数正态和复合（泊松）分布等显著分布的精度。我们的近似是由所谓的正态幂近似的扩展而来的，正态幂近似用于近似随机变量的累积分布函数，它不仅包含所讨论的随机变量的偏度，还包含峭度。我们在数值例子中展示了近似的性能，并与文献中的一些已知近似进行了比较。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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