Precise asymptotics of ruin probabilities for a class of multivariate heavy-tailed distributions

TL;DR

This paper derives precise asymptotic formulas for ruin probabilities in multivariate heavy-tailed random walks, accounting for dependence between components and extending classical univariate results.

Contribution

It provides new asymptotic approximations for multivariate ruin probabilities under subexponential dependence structures, advancing multivariate risk analysis.

Findings

Asymptotic ruin probabilities are characterized for multivariate heavy-tailed distributions.

Dependence between components significantly influences ruin probability estimates.

Results extend classical univariate ruin theory to multivariate heavy-tailed contexts.

Abstract

This article studies asymptotic approximations of ruin probabilities of multivariate random walks with heavy-tailed increments. Under our assumptions, the distributions of the increments are closely connected to multivariate subexponentiality and admit dependence between components. Keywords: subexponential distribution, ruin probability, multivariate random walk