A uniform asymptotic estimate for discounted aggregate claims with subexponential tails

Xuemiao Hao and Qihe Tang

Insurance: Mathematics and Economics, 2008, vol. 43, issue 1, 116-120

Abstract: In this paper we study the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, we obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, we further prove that this formula holds uniformly for all time horizons. In this way, we significantly extend a recent result of Tang [Tang, Q., 2007. Heavy tails of discounted aggregate claims in the continuous-time renewal model. J. Appl. Probab. 44 (2), 285-294].

Date: 2008
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