Enhancing Multivariate Claim Regression with Gaussian Mixture Copula Clustering
Michelle Xia, Lei Hua · North American Actuarial Journal · 2025
Claim analytics usually involves regression on multivariate claims outcomes for the purposes of claim prediction and management. Dependence modeling for different claim outcomes is an important task in claim analytics due to the variety of dependence structures existing among claims outcomes. Motivated by the unique heterogeneous dependence structure shown in the fitted cumulative distribution functions of auto bodily injury, property damage, and vehicle damage losses from marginal claim regression, we propose multivariate claim regression with the Gaussian mixture copula (GMC) that allows identification of underlying claim clusters. The model allows for flexible dependence structures, non-Gaussian marginal distributions, and predictors that may differ by claims outcomes. Using an auto insurance claims dataset, we perform multivariate regression analysis of auto bodily injury, property damage, and vehicle damage claims, with the GMC capturing the underlying claim clusters. Using clusters derived from GMC clustering for training data and random forest cluster prediction for test data, we illustrate that regression tailored to specific clusters can greatly enhance the accuracy for both in-sample and out-of-sample prediction of individual and aggregate claims.