Journal of Statistical and Econometric Methods

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

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• 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.

   

  JEL classification numbers: C14, G22.

  Keywords: Premium, Generalized Additive Models, Dependence, Splines, Frequency, Severity.