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We review two complementary mixture-based clustering approaches for modeling unobserved heterogeneity in an insurance portfolio: the generalized linear mixed cluster-weighted model (CWM) and mixture-based clustering for an ordered stereotype model (OSM). The latter is for modeling of ordinal variables, and the former is for modeling losses as a function of mixed-type of covariates. The article extends the idea of mixture modeling to a multivariate classification for the purpose of testing unobserved heterogeneity in an insurance portfolio. The application of both methods is illustrated on a well-known French automobile portfolio, in which the model fitting is performed using the expectation-maximization (EM) algorithm. Our findings show that these mixture-based clustering methods can be used to further test unobserved heterogeneity in an insurance portfolio and as such may be considered in insurance pricing, underwriting, and risk management.

On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio