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Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims

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  • Tingting Chen
  • Anthony Francis Desmond
  • Peter Adamic

Abstract

This paper examines the problem of accurately estimating the expected value and variance of aggregate claims for each policyholder. Through an appropriate statistical model to estimate the pure premium, an insurer can find niche markets to operate competitively and profitably. To this end, the framework of generalized linear models (GLMs) for aggregate claims is extended to encompass a species of frequentist generalized additive models (GAMs) based on cubic penalized regression splines. The new structure could allow for the incorporation of more flexible nonlinear and/or nonparametric trend terms for the marginal claim frequency, conditional claim severity, and finally for Tweedie modelling as well. This nonparametric approach is illustrated through simulation and applied to an automobile insurance dataset. A juxtaposition of hypothesis test results, AIC values, and attendant graphical diagnostics effectively demonstrate that the GAMs under both the independent and dependent settings give a better fit than the GLM approach. Â JEL classification numbers: C14, G22.

Suggested Citation

  • Tingting Chen & Anthony Francis Desmond & Peter Adamic, 2023. "Generalized Additive Modelling of Dependent Frequency and Severity Distributions for Aggregate Claims," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(4), pages 1-1.
    • Handle: RePEc:spt:stecon:v:12:y:2023:i:4:f:12_4_1
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    References listed on IDEAS

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    More about this item

    Keywords

    Premium; Generalized Additive Models; Dependence; Splines; Frequency; Severity.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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