ASYMPTOTIC TAIL PROBABILITY FOR THE DISCOUNTED AGGREGATE SUMS IN A TIME DEPENDENT RENEWAL RISK MODEL

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 heavy-tailed 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.