Uniform asymptotic estimates for ruin probabilities of a multidimensional risk model with cadlag returns and multivariate heavy tailed claims

TL;DR

This paper derives uniform asymptotic estimates for ruin probabilities in a multidimensional risk model with heavy-tailed, dependent claim vectors and cadlag returns, applicable over finite and infinite time horizons.

Contribution

It provides the first uniform asymptotic estimates for ruin probabilities in a multivariate heavy-tailed risk model with complex dependence structures.

Findings

Asymptotic ruin probabilities are estimated uniformly over finite time horizons.

Results extend to models with multivariate regular variation claims.

Estimates account for weak dependence and arbitrary component dependence.

Abstract

We study a multidimensional renewal risk model, with common counting process and cadlag returns. Considering that the claim vectors have common distribution from some multivariate distribution class with heavy tail, are mutually weakly dependent, and each one has arbitrarily dependent components, we obtain uniformly asymptotic estimations for the probability of entrance of discounted aggregate claims into a some rare sets, over a finite time horizon. Direct consequence of the claim behavior is the estimation of the ruin probability of the model in some ruin sets. Further, restricting the distribution class of the claim vectors in the multivariate regular variation, the estimations still hold uniformly over the whole time horizon.