标题： 评估基于分位数的风险度量估计量的精度 显示英文标题

标题： Evaluating the Precision of Estimators of Quantile-Based Risk Measures

摘要： 本文研究了基于分位数的风险度量（风险价值、预期损失、谱风险度量）估计量的精度。首先解决了如何估计这些估计量精度的问题，并提出了一种蒙特卡洛方法，该方法克服了现有方法的一些局限性。然后研究了风险估计量的分布，并给出了模拟结果，表明在通常可获得的样本量下，依赖渐近正态性结果的常见做法可能不可靠。最后，研究了不同风险估计量的精度与基础损失（或收益）分布之间的关系，并得出了若干有用的结论。 显示英文摘要

摘要： This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions.