英文标题：
《Asymptotic Analysis for Spectral Risk Measures Parameterized by
  Confidence Level》
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作者：
Takashi Kato
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最新提交年份：
2017
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英文摘要：
  We study the asymptotic behavior of the difference $\\Delta \\rho ^{X, Y}_\\alpha := \\rho _\\alpha (X + Y) - \\rho _\\alpha (X)$ as $\\alpha \\rightarrow 1$, where $\\rho_\\alpha $ is a risk measure equipped with a confidence level parameter $0 < \\alpha < 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where $\\rho _\\alpha $ is the value-at-risk (VaR) at $\\alpha $, is treated in Kato (2017). This paper investigates the case where $\\rho _\\alpha $ is a spectral risk measure that converges to the worst-case risk measure as $\\alpha \\rightarrow 1$. We give the asymptotic behavior of the difference between the marginal risk contribution and the Euler contribution of $Y$ to the portfolio $X + Y$. Similarly to Kato (2017), our results depend primarily on the relative magnitudes of the thicknesses of the tails of $X$ and $Y$. We also conducted a numerical experiment, finding that when the tail of $X$ is sufficiently thicker than that of $Y$, $\\Delta \\rho ^{X, Y}_\\alpha $ does not increase monotonically with $\\alpha$ and takes a maximum at a confidence level strictly less than $1$.
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中文摘要：
我们研究了差分$\\Delta\\rho ^{X，Y}\\uAlpha的渐近行为：=\\rho\\uAlpha（X+Y）-\\rho\\uAlpha（X）$作为$\\alpha\\rightarrow 1$，其中$\\rho\\uAlpha$是一个带有置信水平参数$0<\\alpha<1$的风险度量，其中$X$和$Y$是尾部概率函数有规律变化的非负随机变量。加藤（2017）处理了$\\ rho \\u \\ alpha$为$\\ alpha$的风险价值（VaR）的情况。本文研究了$\\ rho \\u \\ alpha$是一个谱风险度量，它收敛到最坏情况下的风险度量$\\ alpha \\ rightarrow 1$。我们给出了边际风险贡献与欧拉贡献之差的渐近行为。与加藤（2017）类似，我们的结果主要取决于$X$和$Y$尾部厚度的相对大小。我们还进行了一个数值实验，发现当$X$的尾部比$Y$的尾部足够厚时，$\\ Delta\\rho ^{X，Y}\\uAlpha$不会随$\\ alpha$单调增加，并且在严格小于1$的置信水平上取最大值。
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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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