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Gamma Mixture Density Networks and their application to modelling insurance claim amounts

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  • Delong, Łukasz
  • Lindholm, Mathias
  • Wüthrich, Mario V.

Abstract

We discuss how mixtures of Gamma distributions with mixing probabilities, shape and rate parameters depending on features can be fitted with neural networks. We develop two versions of the EM algorithm for fitting so-called Gamma Mixture Density Networks, which we call the EM network boosting algorithm and the EM forward network algorithm, and we test their implementation together with the choices of hyperparameters. A simulation study shows that our algorithms perform very well on synthetic data sets. We further illustrate the application of the Gamma Mixture Density Network on a real data set of motor insurance claim amounts and conclude that Gamma Mixture Density Networks can improve the fit of the regression model and the predictions of the claim severities used for rate-making compared to classical actuarial techniques.

Suggested Citation

  • Delong, Łukasz & Lindholm, Mathias & Wüthrich, Mario V., 2021. "Gamma Mixture Density Networks and their application to modelling insurance claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 240-261.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:240-261
    DOI: 10.1016/j.insmatheco.2021.08.003
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    References listed on IDEAS

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    2. Fissler, Tobias & Merz, Michael & Wüthrich, Mario V., 2023. "Deep quantile and deep composite triplet regression," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 94-112.

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    More about this item

    Keywords

    Expectation-maximization algorithm; Neural networks; Mixtures of distributions; Regression models; Rate-making;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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