标题： 基于尾部价值-at-风险的部分随机比较 显示英文标题

标题： On partial stochastic comparisons based on tail values at risk

摘要： 在风险理论中，金融资产回报通常服从重尾分布。 投资者和风险管理师过去常常通过整个置信水平范围上的风险度量（如在险价值或尾部在险价值）来避免暴露于过大的风险。 本文分析了从某个置信水平及其之后的尾部在险价值之间的比较，这是一个合理的标准，当我们将重点放在大损失上或者我们无法在所有置信水平上给出完整的排序时。 提出了一组由 $p_0\in(0,1)$ 指标索引的随机序。 我们研究了这些序的性质以及它们与其他经典准则（如递增凸序和尾部凸序）的关系，并对某些参数化分布族进行了排序。 最后，还给出了两个使用真实数据集的应用实例。 显示英文摘要

摘要： In risk theory, financial asset returns often follow heavy-tailed distributions. Investors and risk managers used to compare risk measures as the value at risk or tail value at risk in order over the whole confidence levels to avoid the exposure to to large risks. In this paper we analyze the comparison between tail values at risk from a confidence level and beyond which is a reasonable criterion when we are focused on large losses or simply we cannot give a complete ordering over all the confidence levels. A family of stochastic orders indexed by $p_0\in(0,1)$ is proposed. We study their properties and connections with other classical criteria as the increasing convex and tail convex orders and we rank some parametrical families of distributions. Finally, two applications with real datasets are given as well.