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Precise large deviations for the prospective-loss process. (English) Zbl 1028.60024

Summary: We propose a customer-arrival-based insurance risk model, in which customers’ 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.

MSC:

60F10 Large deviations
60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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