Statistical Learning Algorithms Applied to Automobile Insurance Ratemaking

We recently conducted a research project for a large North American automobile insurer. This study was the most exhaustive ever undertaken by this particular insurer and lasted over an entire year. We analyzed the discriminating power of each variable used for ratemaking. We analyzed the performance of several models within five broad categories: linear regressions, generalized linear models, decision trees, neural networks and support vector machines. In this paper, we present the main results of this study. We qualitatively compare models and show how neural networks can represent high-order nonlinear dependencies with a small number of parameters, each of which is estimated on a large proportion of the data, thus yielding low variance. We thoroughly explain the purpose of the nonlinear sigmoidal transforms which are at the very heart of neural networks’ performances. The main numerical result is a statistically significant reduction in the out-of-sample meansquared error using the neural network model and our ability to substantially reduce the median premium by charging more to the highest risks. This in turn can translate into substantial savings and financial benefits for an insurer. We hope this paper goes a long way in convincing actuaries to include neural networks within their set of modeling tools for ratemaking.