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Modelling Claim Frequency in Vehicle Insurance

Author

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  • Jiří Valecký

    (Department of Finance, Faculty of Economics, VŠB-TU Ostrava, Sokolská tř. 33, 701 21 Ostrava, Czech Republic)

Abstract

The paper is focused on modelling claim frequency and extends the work of Kafková and Křivánková, 2014 (Kafková, S., Křivánková, L. 2014. Generalized linear models in vehicle insurance. Acta universitatis agriculturae et silviculturae mendelianae brunensis, 62(2): 383-388). We showed that overdispersion, non-linear systematic component and interacted rating factors should be considered when the claim frequency is modelled. We detected overdispersion in the Poisson model and employed the negative-binomial model to show that considering heterogeneity over insurance policies yields better fit of the model. We also analysed the linear effect of continuous rating factors and their mutual influences. We showed that non-linearity and interactions between rating factors yield the better fit of the model, as well as new findings related to the analysis of claim frequency. All empirical models were estimated on the insurance portfolio of Czech insurance company collected during the years 2004-2008.

Suggested Citation

  • Jiří Valecký, 2016. "Modelling Claim Frequency in Vehicle Insurance," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 64(2), pages 683-689.
    • Handle: RePEc:mup:actaun:actaun_2016064020683
    DOI: 10.11118/actaun201664020683
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    References listed on IDEAS

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    1. Renshaw, Arthur E., 1994. "Modelling the Claims Process in the Presence of Covariates," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 265-285, November.
    2. Martin Branda, 2014. "Optimization Approaches to Multiplicative Tariff of Rates Estimation in Non-Life Insurance," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-17.
    3. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
    4. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    5. Vern T. Farewell & Brian D.M. Tom & Patrick Royston, 2004. "The Impact of Dichotomization on the Efficiency of Testing for an Interaction Effect in Exponential Family Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 822-831, January.
    6. Zaks, Yaniv & Frostig, Esther & Levikson, Benny, 2006. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 161-185, May.
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