AI 中文总结
研究FGM相依结构下条件高阶矩相干风险度量的二阶渐近展开，利用极值理论等推导展开式，相比一阶结果能更准确捕捉高阶行为和相依效应，经模拟和实证应用验证了二阶方法的优势。
AI 中文摘要
本文研究了在Farlie-Gumbel-Morgenstern（FGM）相依结构下条件高阶矩（CoHM）相干风险度量的二阶渐近展开，刻画了主要损失风险与参考风险之间的弱传染。假设主要风险属于Fréchet、Weibull或Gumbel最大吸引域，利用极值理论和二阶正则变化理论系统地推导二阶渐近展开。与现有一阶结果相比，改进后的近似更准确地捕捉高阶尾部行为和相依效应。数值模拟证实二阶渐近性大幅降低近似误差，特别是在极端置信水平下。对保险索赔数据的实证应用进一步说明了二阶方法的实际优越性。
英文摘要
This paper investigates second-order asymptotic expansions for the conditional higher moment (CoHM) coherent risk measure under a Farlie-Gumbel-Morgenstern (FGM) dependence structure, capturing a weak contagion between a primary loss risk and a reference risk. Assuming that the primary risk belongs to the Fréchet, Weibull, or Gumbel maximum domain of attraction, we systematically derive second-order asymptotic expansions using extreme value theory and second-order regular variation theory. Compared with existing first-order results, our refined approximations capture higher-order tail behavior and dependence effects more accurately. Numerical simulations confirm that the second-order asymptotics substantially reduce approximation errors, especially at extreme confidence levels. Empirical applications to insurance claim data further illustrate the practical superiority of the second-order approach.
