Uniformly asymptotic behavior for the tail probability of discounted aggregate claims in the time-dependent risk model with upper tail asymptotically independent claims

Xijun Liu and Qingwu Gao

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 18, 5341-5354

Abstract: In this paper, we consider the tail behavior of discounted aggregate claims in a dependent risk model with constant interest force, in which the claim sizes are of upper tail asymptotic independence structure, and the claim size and its corresponding inter-claim time satisfy a certain dependence structure described by a conditional tail probability of the claim size given the inter-claim time before the claim occurs. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all times in a finite interval. Moreover, we prove that if the claim size distribution belongs to the consistent variation class, the formula holds uniformly for all times in an infinite interval.

Date: 2016
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DOI: 10.1080/03610926.2014.942431

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