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Application of the Generalized Linear Models in Actuarial Framework

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  • Murwan H. M. A. Siddig

Abstract

This paper aims to review the methodology behind the generalized linear models which are used in analyzing the actuarial situations instead of the ordinary multiple linear regression. We introduce how to assess the adequacy of the model which includes comparing nested models using the deviance and the scaled deviance. The Akiake information criterion is proposed as a comprehensive tool for selecting the adequate model. We model a simple automobile portfolio using the generalized linear models, and use the best chosen model to predict the number of claims made by the policyholders in the portfolio.

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  • Murwan H. M. A. Siddig, 2016. "Application of the Generalized Linear Models in Actuarial Framework," Papers 1611.02556, arXiv.org.
    • Handle: RePEc:arx:papers:1611.02556
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    References listed on IDEAS

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    1. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, February.
    4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    5. Verrall, Richard, 1996. "Claims reserving and generalised additive models," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 31-43, December.
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