Abstract
In this paper, we consider a size-dependent renewal risk model with stopping time claim-number process. In this model, we do not make any assumption on the dependence structure of claim sizes and inter-arrival times. We study large deviations of the aggregate amount of claims. For the subexponential heavy-tailed case, we obtain a precise large-deviation formula; our method substantially relies on a martingale for the structure of our models.
Highlights
4 Conclusions As was remarked by a few researchers in the area, precise large-deviation results of sizedependent renewal risk models are useful for evaluating some risk measures such as the conditional tail expectation of the aggregate amount of claims from a large insurance portfolio
This indicates that the aggregate amount of St∗ defined by ( . ) does not affect the asymptotic behavior of the large deviations
Summary
The number of claims is defined Nt∗ is a stopping time. The aggregate amount of claims over the [ , t] is of the form We study large deviations of St∗ in ). We only consider the case of heavy-tailed claimsize distributions.
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