  The aim of this paper is to present a mixture composite regression model for
claim severity modelling. Claim severity modelling poses several challenges
such as multimodality, heavy-tailedness and systematic effects in data. We
tackle this modelling problem by studying a mixture composite regression model
for simultaneous modeling of attritional and large claims, and for considering
systematic effects in both the mixture components as well as the mixing
probabilities. For model fitting, we present a group-fused regularization
approach that allows us for selecting the explanatory variables which
significantly impact the mixing probabilities and the different mixture
components, respectively. We develop an asymptotic theory for this regularized
estimation approach, and fitting is performed using a novel Generalized
Expectation-Maximization algorithm. We exemplify our approach on real motor
insurance data set.
