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

38 Pages Posted: 23 Nov 2020 Last revised: 14 Apr 2021

See all articles by Lukasz Delong

Lukasz Delong

Warsaw School of Economics (SGH) - Institute of Econometrics

Mathias Lindholm

Stockholm University

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: October 5, 2020

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.

Keywords: Expectation-Maximization, neural networks, boosting, mixtures of distributions

JEL Classification: G22, C45

Suggested Citation

Delong, Lukasz and Lindholm, Mathias and Wuthrich, Mario V., Gamma Mixture Density Networks and their application to modelling insurance claim amounts (October 5, 2020). Available at SSRN: https://ssrn.com/abstract=3705225 or http://dx.doi.org/10.2139/ssrn.3705225

Lukasz Delong (Contact Author)

Warsaw School of Economics (SGH) - Institute of Econometrics ( email )

Niepodleglosci 164
Warsaw, 02-554
Poland

Mathias Lindholm

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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