Tail Asymptotic of Heavy-Tail Risks with Elliptical Copula

TL;DR

This paper analyzes the tail behavior of multivariate heavy-tailed risks with elliptical dependence, providing asymptotic probabilities, regular variation properties, and practical applications in finance and insurance.

Contribution

It characterizes the asymptotic tail risks and multivariate regular variation for elliptical copula-based risks, extending understanding of dependence in heavy-tailed distributions.

Findings

Tail probabilities depend on covariance matrix and tail decay rate

Regular variation property is established for the multivariate risks

Numerical simulations and real data demonstrate practical relevance

Abstract

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.