Global Sensitivity Analysis of Predictive Models: Shapley Effects in Rating Systems

The ratemaking process is a key issue in insurance pricing. It consists in pooling together policyholders with similar risk profiles into rating classes and assigning the same premium for policyholders in the same class. In actuarial practice, rating systems are typically not based on all risk factors but rather only some of factors are selected to construct the rating classes. The objective of this presentation is to investigate the selection of risk factors in order to construct rating classes that exhibit maximum internal homogeneity. For this selection, we adopt the Shapley effects from global sensitivity analysis. We present these sensitivity indices for the interpretability of predictive models and we apply them to construct rating classes. We connect these importance measures to the intra-class variability and heterogeneity of the rating classes. To verify the appropriateness of this procedure, we introduce a measure of heterogeneity specifically designed to compare rating systems with a different number of classes. Using a well-known car insurance dataset, we show that the rating system constructed with the Shapley effects is the one minimizing this heterogeneity measure.