Asymptotic tail probability for the discounted aggregate sums in a time dependent renewal risk model

Abstract

This paper presents an extension of the classical compound Poisson risk model in which the inter-claim time arrivals and the claim amounts are structurally dependent. We derive the corresponding asymptotic tail probabilities for the discounted aggregate claims in a finite insurance contract under constant force of interest. The dependence assumption between the inter-claim times and the claim amounts is well suited for insurance contracts during extreme and catastrophic events. Based on the existing literature, we use heavytailed distributions for the discounted aggregate claims and derive the extreme value at risk (minimum capital requirement). Our results, based on a case study of ten million simulations, show that the independence assumption between the inter-claim times and the claim amounts lead to underestimating the minimum capital requirement proposed by the regulatory authorities.