发表机构
University of Bremen（不来梅大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对e-backtesting程序，提出了检测预期短缺低估所需样本量的确定方法，推导了样本量近似下界，讨论了近似局限性并与蒙特卡洛模拟结果对比，还推广了e-backtesting至贝叶斯对风险测度。
AI 中文摘要
我们提出一种方法，用于在应用新近提出的e-backtesting（电子回溯测试）程序时，确定以规定功效检测预期短缺（expected shortfall）低估所需的样本量。我们考虑的场景为：p水平的风险价值（value-at-risk）始终估计正确，而真实预期短缺与风险价值的差值被给定因子r低估。我们表明，利用为回溯p水平预期短缺而提出的回溯测试e统计量的结构，可通过考虑独立同分布伯努利随机变量序列，推导所需样本量的近似下界。我们还讨论了该近似的潜在局限性，并将所得样本量要求与实际应用中通过蒙特卡洛模拟得到的结果进行比较。此外，我们给出了e-backtesting程序的推广，特别是针对构成贝叶斯对（Bayes pairs）的风险测度的推广。
英文摘要
We present an approach for determining sample sizes required to detect underestimations of the expected shortfall with a prescribed power when applying the recently proposed e-backtesting procedure. We consider scenarios in which the value-at-risk at level $p$ is always estimated correctly, while the difference between the true expected shortfall and the value-at-risk is underestimated by a given factor $r$. We show that exploiting the structure of the backtest e-statistic proposed for backtesting the expected shortfall at level $p$ enables the derivation of approximate lower bounds for the required sample sizes by considering a sequence of independent and identically distributed Bernoulli random variables. We also discuss potential limitations of this approximation and compare the resulting sample size requirements with those obtained in practical applications using Monte Carlo simulations. Furthermore, we present generalizations of the e-backtesting procedure, in particular to risk measures which constitute Bayes pairs.
