英文标题：
《Relative Bound and Asymptotic Comparison of Expectile with Respect to
  Expected Shortfall》
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作者：
Samuel Drapeau and Mekonnen Tadese
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最新提交年份：
2020
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英文摘要：
  Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the confidence level goes to $1$ in terms of extreme value distributions. We use concentration inequalities to illustrate that the estimation of value at risk requires larger sample size than expected shortfall and expectile for heavy tail distributions when $\\alpha$ is close to $1$. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile and some simulation results for some classical distributions.
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中文摘要：
就尾部风险评估而言，与整个行业的预期缺口相比，Expectile具有一些有趣的特性。我们利用对偶结果以及与优化确定性等价的联系来研究期望值和期望不足之间的关系。期望值的上下界是根据期望值的不足得到的，同时也是根据期望值的不足得到的期望值的特征。此外，我们还研究了在极值分布下，当置信水平达到1美元时，期望值相对于期望短缺的渐近行为。我们使用集中度不等式来说明，当$\\ alpha$接近1$时，风险价值的估计需要比预期短缺和重尾分布预期更大的样本量。为了说明期望值的表达式，我们还提供了期望值的显式或半显式表达式以及一些经典分布的模拟结果。
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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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