Regressione a Quantili e Misure di Sensibilità Globali per la Tariffazione Assicurativa

The ratemaking process is a key task in the insurance field and consists in assigning to each risk class a price that reflects the riskiness of the insured. In this thesis, we focus on the problem of finding a method to select the more important risk factors to construct a rating system for insurance pricing. To this aim, firstly we compute the loaded premium at an individual level. Then, we apply global sensitivity measures, in particular Shapley effects, to find which are the covariates (risk factors) that explain together as much variability as possible of the insurance price previously found. It is a novelty since Shapley effects have never been used in insurance ratemaking. Finally, we construct risk classes aggregating policyholders that show the same values of the discovered covariates. To measure class homogeneity, we propose to use the coefficient of variation. In particular, we provide a numerical application using a car insurance dataset. We show a comparison of rating systems constructed with different risk factors using the weighted mean of variation coefficients.