We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the asymptotic tail risk probabilities and characterize the multivariate regular variation property. The results demonstrate how the rate of decay of probabilities on tail sets varies in tail sets and the covariance matrix of the elliptical copula. The theoretical results are well illustrated by typical examples and numerical simulations. A real data application shows its advantages in a more flexible dependence structure to characterize joint insurance losses.

翻译：本文考虑一类具有重尾边缘分布和I型椭圆相依结构的多变量分布族。这类风险在金融、保险、环境及生物统计应用中较为常见。我们获得了尾部风险概率的渐近值，并刻画了多元正则变化性质。结果表明，尾部集合上概率衰减速率如何随尾部集合及椭圆Copula的协方差矩阵变化而变化。通过典型实例和数值模拟充分验证了理论结果。实际数据应用表明，该模型在刻画联合保险损失方面具有更灵活的相依结构优势。