Precise large deviations of sums of widely dependent random variables and its applications

TL;DR

This paper derives precise large deviation results for sums of widely dependent random variables with specific tail behaviors and applies these findings to insurance and reinsurance risk assessments.

Contribution

It provides new asymptotic estimates for large deviations of dependent sums with dominatedly or consistently varying tails, extending classical results.

Findings

Asymptotic estimates for reinsurance and insurance risk measures

Precise large deviation results for dependent variables with specific tail distributions

Applications to ruin probabilities in insurance models

Abstract

In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on $(-\infty,\infty)$. Then we apply the results to reinsurance and insurance and give some asymptotic estimates on proportional reinsurance, random-time ruin probability and the finite-time ruin probability.