Solvency tuned premium for a composite loss distribution.

Summary A parametric framework is proposed to model both attritional and atypical claims for insurance pricing. This model relies on a classical Generalized Linear Model for attritional claims and a non-standard Generalized Pareto distribution regression model for atypical claims. Maximum likelihood estimators (closed-form for the Generalized Linear Model part and computed with Iterated Weighted Least Square procedure for the Generalized Pareto distribution regression part) are proposed to calibrate the model. Two premium principles (expected value principle and standard deviation principle) are computed on a real data set of fire warranty of a corporate line-of-business. In our methodology, the tuning of the safety loading in the two premium principles is performed to meet a solvency constraint so that the premium caps a high-level quantile of the aggregate annual claim distribution over a reference portfolio.