On the random-time and finite-time ruin probability for widely dependent claim sizes and inter-arrival times

TL;DR

This paper derives asymptotic estimates for ruin probabilities in a renewal risk model with highly dependent claim sizes and inter-arrival times, advancing understanding of risk in complex dependent systems.

Contribution

It introduces new asymptotic estimation methods for ruin probabilities in models with widely dependent claim sizes and inter-arrival times, using large deviation and renewal theory.

Findings

Asymptotic estimation of random-time ruin probability

Uniform asymptotic estimation of finite-time ruin probability

Applicable to models with widely dependent claim variables

Abstract

Using the results of precise large deviation and renewal theory for widely dependent random variables, this paper obtains the asymptotic estimation of the random-time ruin probability and the uniform asymptotic estimation of finite-time ruin probability for a nonstandard renewal risk model, in which both claim sizes and the inter-arrival times of claim sizes are widely dependent.