Asymptotics for a delay-claim risk model with diffusion, dependence structures and constant force of interest

Abstract

In the paper, we consider an insurance risk model perturbed by diffusion with constant force of interest, where each main claim may induce a delayed claim, called a by-claim. If the main claims and by-claims form a sequence of pairwise quasi-asymptotically independent random variables with long tails and dominatedly varying tails, and the main-claim arrival process is an arbitrary counting process, we obtain a uniformly asymptotic formula for finite-time ruin probability for times in a finite interval. Particularly, with a certain dependence structure among the inter-arrival times of main claims, the formula holds uniformly for all times when the claim sizes are consistently-varying-tailed, where the result obtained also covers an asymptotic formula for the infinite-time ruin probability.