Thierry Bauwelinckx

On a multilevel hierarchical credibility algorithm

Abstract A hierarchical credibility model is considered with multiple levels for diagonal covariance matrices. An algorithm for the iterative evaluation of the structure parameters is given. This extends a result of Buhlmann and Jewell (1987) on hierarchical credibility to the evaluation of the structure parameters.

The practical application of credibility theory

Abstract It is shown how credibility theory can be applied to solve some realistic insurance problems. The applications given in this contribution emerge from the opportunity the authors had in implementing the software packet CRAC 2.0 in different insurance companies. While some of the applications are described in general, the introduction of a franchise deductible for credit insurance is investigated in more detail.

A new approach for loaded credibility premiums

Abstract In this contribution a new technique is developed for estimating credibility premiums for risks, containing a fraction of the variance of the risk as loading on the net risk premium. This method provides us with another approach to the known results for credibility loaded premiums, not having the drawback of estimating an approximation of the so-called fluctuation part. In addition the present investigation provides us with an elegant extension to loaded premiums in the hierarchical credibility model. The results are obtained in the framework of semilinear hierarchical credibility theory. As a byproduct the so-called optimal semilinear credibility result is extended to the case of Esscher premiums. In this contribution also the pseudo-estimators, to be solved iteratively for the structural parameters appearing in the variance-loaded model, are given.