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Modelling repeated insurance claim frequency data using the generalized linear mixed model

Author

Listed:
  • Kelvin Yau
  • Karen Yip
  • H. K. Yuen

Abstract

Most of the methods used to estimate claim frequency rates in general insurance have assumed that data are independent. However, it is not uncommon for information stored in the database of an insurance company to contain previous years' claim data from each policyholder. We consider the application of the generalized linear mixed model approach to the analysis of repeated insurance claim frequency data in which a conditionally fixed random effect vector is incorporated explicitly into the linear predictor to model the inherent correlation. A motor insurance data set is used as the basis for simulation to demonstrate the advantages of the method. Ignoring the underlying association for observations within the same policyholder results in an underestimation of the standard error of the parameter estimates and a remarkable reduction in the prediction accuracy. The method provides a viable alternative for incorporating repeated claim experience that enables the revision of rates in general insurance.

Suggested Citation

  • Kelvin Yau & Karen Yip & H. K. Yuen, 2003. "Modelling repeated insurance claim frequency data using the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 857-865.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:8:p:857-865
    DOI: 10.1080/0266476032000075949
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    References listed on IDEAS

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    Cited by:

    1. Norbert Paska, 2018. "Zastosowanie modeli ZINB GLMM z efektem losowym agenta w taryfikacji ubezpieczeń majątkowych," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 53, pages 63-76.
    2. Shengkun Xie & Chong Gan, 2023. "Estimating Territory Risk Relativity Using Generalized Linear Mixed Models and Fuzzy C -Means Clustering," Risks, MDPI, vol. 11(6), pages 1-20, May.
    3. GÓMEZ GARCÍA, J.Mª & PELÁEZ FERMOSO, F.J. & y GARCÍA GONZÁLEZ, A., 2005. "Repercusiones del envejecimiento demográfico sobre el sistema público de pensiones en Castilla y León," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 23, pages 235-253, Abril.
    4. Calcetero Vanegas, Sebastián & Badescu, Andrei L. & Lin, X. Sheldon, 2024. "Effective experience rating for large insurance portfolios via surrogate modeling," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 25-43.
    5. Sebastian Calcetero-Vanegas & Andrei L. Badescu & X. Sheldon Lin, 2022. "Effective experience rating for large insurance portfolios via surrogate modeling," Papers 2211.06568, arXiv.org, revised Jun 2024.

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