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Precise large deviations for the prospective-loss process

  • Kai W. Ng (a1), Qihe Tang (a2), Jiaan Yan (a3) and Hailiang Yang (a1)
Abstract

In this paper, 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.

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Corresponding author
Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong.
∗∗ Postal address: Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.
∗∗∗ Postal address: Academy of Mathematics and System Sciences, The Chinese Academy of Sciences, Beijing 100080, P. R. China.
∗∗∗∗ Email address: hlyang@hku.hk
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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