Telematics Combined Actuarial Neural Networks for Cross-Sectional and Longitudinal Claim Count Data

TL;DR

This paper introduces a novel combined actuarial neural network (CANN) framework for vehicle insurance claim count data, integrating classical models with neural networks to improve predictive accuracy and interpretability.

Contribution

The paper develops a new CANN approach that incorporates longitudinal dependencies and telematics data into claim count modeling, enhancing performance over traditional methods.

Findings

CANN models outperform log-linear models with engineered features.

Inclusion of longitudinal data improves model accuracy.

Neural network component captures complex driving behavior patterns.

Abstract

We present novel cross-sectional and longitudinal claim count models for vehicle insurance built upon the Combined Actuarial Neural Network (CANN) framework proposed by Mario W\"uthrich and Michael Merz. The CANN approach combines a classical actuarial model, such as a generalized linear model, with a neural network. This blending of models results in a two-component model comprising a classical regression model and a neural network part. The CANN model leverages the strengths of both components, providing a solid foundation and interpretability from the classical model while harnessing the flexibility and capacity to capture intricate relationships and interactions offered by the neural network. In our proposed models, we use well-known log-linear claim count regression models for the classical regression part and a multilayer perceptron (MLP) for the neural network part. The MLP part is used to process telematics car driving data given as a vector characterizing the driving behavior of each insured driver. In addition to the Poisson and negative binomial distributions for cross-sectional data, we propose a procedure for training our CANN model with a multivariate negative binomial (MVNB) specification. By doing so, we introduce a longitudinal model that accounts for the dependence between contracts from the same insured. Our results reveal that the CANN models exhibit superior performance compared to log-linear models that rely on manually engineered telematics features.