Uniform asymptotics for a multidimensional renewal risk model with multivariate subexponential claims

TL;DR

This paper develops uniform asymptotic estimates for the probability of large aggregate claims in a multidimensional risk model with subexponential claim distributions, considering dependence and interest factors.

Contribution

It introduces locally uniform asymptotic estimations for rare event probabilities in a multivariate renewal risk model with subexponential claims and dependence structures.

Findings

Derived asymptotic estimations for aggregate claims entering rare sets.

Established uniform asymptotics over all time horizons.

Provided examples of multivariate heavy-tailed distributions beyond regular variation.

Abstract

In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of dependent components belonging to the class of multivariate subexponential distributions. We establish locally uniform asymptotic estimations for the entrance probability of the discounted aggregate claims into some rare sets, and further derive asymptotic estimations uniformly over all the time horizons. Furthermore, we present some distribution examples that belong to these multivariate heavy-tailed distribution classes, which are not restricted only to the case of multivariate regular variation.