Precise large deviations for a customer-based individual risk model

In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d. heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV (extended regular variation). Lundberg type limiting results on the finite time ruin probabilities are also investigated.