Subexponential tails of discounted aggregate claims in a time-dependent renewal risk model

Jinzhu Li, Qihe Tang, Rong Wu
2010 Advances in Applied Probability  
Consider a continuous-time renewal risk model with a constant force of interest. We assume that claim sizes and interarrival times correspondingly form a sequence of independent and identically distributed random pairs and that each pair obeys a dependence structure described via the conditional tail probability of a claim size given the interarrival time before the claim. We focus on determining the impact of this dependence structure on the asymptotic tail probability of discounted aggregate
more » ... scounted aggregate claims. Assuming that the claim size distribution is subexponential, we derive an exact locally uniform asymptotic formula, which quantitatively captures the impact of the dependence structure. When the claim size distribution is extended regularly varying tailed, we show that this asymptotic formula is globally uniform.
doi:10.1239/aap/1293113154 fatcat:434mzeag6vdm7m7ov3qtoaeygy