Nesting Classical Actuarial Models into Neural Networks

27 Pages Posted: 25 Jan 2019

Date Written: January 22, 2019


Neural network modeling often suffers the deficiency of not using a systematic way of improving classical statistical regression models. In this tutorial we exemplify the proposal of the editorial of ASTIN Bulletin 2019/1. We embed a classical generalized linear model into a neural network architecture, and we let this nested network approach explore model structure not captured by the classical generalized linear model. In addition, if the generalized linear model is already close to optimal, then the maximum likelihood estimator of the generalized linear model can be used as initialization of the fitting algorithm of the neural network. This saves computational time because we start the fitting algorithm in a reasonable parameter. As a by-product of our derivations, we present embedding layers and representation learning which often provides a more efficient treatment of categorical features within neural networks than dummy and one-hot encoding.

Keywords: regression model, generalized linear model, neural network model, embedding layer, representation learning, Poisson regression

JEL Classification: G22

Suggested Citation

Schelldorfer, Jürg and Wuthrich, Mario V., Nesting Classical Actuarial Models into Neural Networks (January 22, 2019). Available at SSRN: or

Jürg Schelldorfer

Swiss Re

Mythenquai 50/60
Zurich, 8022

Mario V. Wuthrich (Contact Author)

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092

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