Precise large deviations for the prospective-loss process.

In this paper, we propose a customer-arrival-based insurance risk model, in which customersʹ potential claims are described as independent and identically distributed heavy-tailed random variables and premiums are the same for each policy. We obtain some precise large deviation results for the prospective-loss process under a mild assumption on the random index (in our case, the customer-arrival process), which is much weaker than that in the literature