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The Poisson random effect model for experience ratemaking: Limitations and alternative solutions

Title
The Poisson random effect model for experience ratemaking: Limitations and alternative solutions
Authors
Lee W.Kim J.Ahn J.Y.
Ewha Authors
안재윤
SCOPUS Author ID
안재윤scopus
Issue Date
2020
Journal Title
Insurance: Mathematics and Economics
ISSN
0167-6687JCR Link
Citation
Insurance: Mathematics and Economics vol. 91, pp. 26 - 36
Keywords
Claim frequencyDependenceExperience ratemakingNegative binomial distributionPoisson random-effect model
Publisher
Elsevier B.V.
Indexed
SCIE; SSCI; SCOPUS scopus
Document Type
Article
Abstract
Poisson random effect models with a shared random effect have been widely used in actuarial science for analyzing the number of claims. In particular, the random effect is a key factor in a posteriori risk classification. However, the necessity of the random effect may not be properly assessed due to the dual role of the random effect; it affects both the marginal distribution of the number of claims and the dependence among the numbers of claims obtained from an individual over time. We first show that the score test for the nullity of the variance of the shared random effect can falsely indicate significant dependence among the numbers of claims even though they are independent. To mitigate this problem, we propose to separate the dual role of the random effect by introducing additional random effects to capture the overdispersion part, which are called saturated random effects. In order to circumvent heavy computational issues by the saturated random effects, we choose a gamma distribution for the saturated random effects because it gives the closed form of marginal distribution. In fact, this choice leads to the negative binomial random effect model that has been widely used for the analysis of frequency data. We show that safer conclusions about the a posteriori risk classification can be made based on the negative binomial mixed model under various situations. We also derive the score test as a sufficient condition for the existence of the a posteriori risk classification based on the proposed model. © 2019 Elsevier B.V.
DOI
10.1016/j.insmatheco.2019.12.004
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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