Second Order Asymptotics Formula for Discounted Total Claims with Constant Interest Force

Abstract

In this article, we analyse discounted total claims of insurance company, where the claim-size distribution is second order subexponential and the claim-number forms a renewal process. Using the asymptotic theory of the right-tail probability of randomly weighted sums, we study the right tail probability of discounted aggregate claims, and obtain a second order asymptotic expression, which was established uniformly for any finite-time level. The result is superior to the first order asymptotic formula.