Motivated by the need to correctly rank risky alternatives in many investment, insurance and operations research applications, this paper uses a generalized location and scale framework from utility theory to propose a simple but powerful metric for comparing the estimation error of conceptually different risk measures. In an illustrative application, we obtain this metric — the probability that a risk measure ranks two assets falsely in finite samples — via Monte Carlo simulation for fourteen popular measures of risk and different distributional settings. Its results allow us to highlight interesting risk measure properties such as their relative quality under varying degrees of skewness and kurtosis. Because of the generality of our approach, the error probabilities derived for classic risk measures can serve as a benchmark for newly proposed measures seeking to replace the classic ones in decision making. It also supports the identification of the most suitable risk measures for a given distributional environment.

中文翻译：

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概念上不同风险措施的小样本估计误差比较

出于对许多投资、保险和运筹学应用中的风险替代方案进行正确排序的需要，本文使用效用理论中的广义位置和规模框架，提出了一个简单但强大的度量标准，用于比较概念上不同风险度量的估计误差。在一个说明性的应用程序中，我们通过对 14 种流行的风险度量和不同的分布设置进行蒙特卡罗模拟，获得了这个度量——风险度量在有限样本中错误地对两种资产进行排名的概率。它的结果使我们能够突出有趣的风险度量属性，例如它们在不同程度的偏度和峰度下的相对质量。由于我们方法的普遍性，从经典风险度量中推导出的错误概率可以作为新提议的度量标准，以在决策中取代经典的度量标准。它还支持为给定的分布式环境确定最合适的风险措施。