ABSTRACT As perceived from daily experience together with numerous empirical studies, the multivariate risks demonstrate a strong coherence in the extremal dependence structure especially over the course of financial turmoil or industrial accidents and outbreaks. Under this motivating paradigm, we show the universal asymptotic additivity under upper tail comonotonicity, as the probability level approaching to 1, for Value-at-Risk and Conditional Tail Expectation for a portfolio of fixed number of risks, in which each marginal risk could be any one having a finite endpoint or belonging to one of the three max domains of attraction. Our obtained results do not require the tail equivalence assumption as needed in the existing literature. This resolves a lasting problem in quantitative risk management and covers most distributions commonly encountered in practice.

中文翻译：

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关于尾部共调风险的可加性

摘要从日常经验和大量实证研究中可以看出，多元风险在极端依赖结构中表现出很强的一致性，尤其是在金融动荡或工业事故和爆发的过程中。在这种激励范式下，我们展示了上尾共调下的普遍渐近可加性，随着概率水平接近 1，对于固定数量风险的投资组合的风险价值和条件尾期望，其中每个边际风险可以是任何具有有限端点或属于三个最大吸引力域之一的任何一个。我们获得的结果不需要现有文献中所需的尾部等效假设。