Uniform Asymptotics for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with Pairwise Quasiasymptotically Independent Claims

Abstract

We consider a generalized time-dependent risk model with constant interest force, where the claim sizes are of pairwise quasiasymptotical independence structure, and the claim size and its interclaim time satisfy a dependence structure defined by a conditional tail probability of the claim size given the interclaim time before the claim occurs. As the claim-size distribution belongs to the dominated variation class, we establish some weakly asymptotic formulae for the tail probability of discounted aggregate claims and the finite-time ruin probability, which hold uniformly for all times in a relevant infinite interval.