A Unified Approach for the Modeling of Rating Factors in Workers’ Compensation Insurance
by Ben Stassen, Michel Denuit, Samuel Mahy, Xavier Maréchal and Julien Trufin
Workers’ Compensation is an insurance cover whereby an employer compensates for the lost wages and medical expenses of an employee who is injured on the job. As with other types of insurance, premium rates for workers' compensation policies are calculated according to several different factors. In Belgium, current market practice consists of pricing workers’ compensation based on a hierarchical credibility model, i.e. the Jewell model. Hierarchical credibility models provide a nice hierarchical procedure in the calculation of premiums. First, we produce an expected aggregate claim amount for the whole line of business. Then, we distribute this amount over lower levels (top down approach).
In this paper, we define a new tariff structure for workers’ compensation by combining hierarchical credibility models with a GLMM approach in the final pure premium model. We start with the calculation of a basic pure premium rate in function of some explanatory variables by using a Generalized Linear Mixed Model (which is an extension of the well-known Generalized Linear Models). The advantage of such a model is that we can now fit ordinary rating factors and hierarchical rating factors at the same time. Afterwards, this basic premium rate is adapted according to the client’s history of claims data with the use the Bühlmann-Straub credibility model.