Insurance risk classification with Generalized Gaussian Process Regression models

This paper proposes a new approach to risk classification based on Generalized Gaussian Process Regression (GGPR). The response under consideration obeys a distribution belonging to the Exponential Dispersion (ED) family. It typically corresponds to a claim count or a claim severity in the context of insurance studies. GGPR is a supervised machine learning method with Bayesian flavor. Individual random effects obeying a multivariate Normal distribution are connected with the help of their covariance matrix built from a so-called kernel function. The latter enforces smoothness, borrowing information from similar risk profiles. Bayesian Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) are recovered as special cases, assuming a highly-structured prior covariance matrix. Compared to the existing literature, this paper innovates to account for the specificity of data entering insurance studies. First, proper risk exposures are included in model formulation and development. Second, parameters are estimated by minimizing deviance instead of an approximated loglikelihood. Third, categorical features that are often encountered in insurance data bases are coded with the help of an embedding method based on Burt matrices. Fourth, K-means clustering is used to reduce the dimension of the problem and create model points within large insurance portfolios. Numerical illustrations performed on publicly available insurance data sets illustrate the relevance of the GGPR approach to risk classification. Benchmarked against the classical GLM, the performances of GGPR turn out to be excellent given its reduced number of parameters. This suggests that GGPR nicely enriches the actuarial toolkit by providing preliminary predictions that can then be structured with additive scores like those entering GLMs and GAMs.