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Precise large deviations for the prospective-loss process

Part of: Stochastic processes Applications Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Kai W. Ng ,
Qihe Tang ,
Jiaan Yan  and
Hailiang Yang
Kai W. Ng*
Affiliation:
University of Hong Kong
Qihe Tang*
Affiliation:
University of Amsterdam
Jiaan Yan*
Affiliation:
The Chinese Academy of Sciences, Beijing
Hailiang Yang*
Affiliation:
University of Hong Kong
*
∗ 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.
∗ Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong.
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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.

Keywords

Insurance risk modelpoint processprecise large deviationsubexponentiality

MSC classification

Primary: 60F10: Large deviations 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks
Secondary: 60K10: Applications (reliability, demand theory, etc.) 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 391 - 400
Copyright
Copyright © Applied Probability Trust 2003 

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