Journal of computational and applied mathematics vol:37 issue:1-3 pages:301-314
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.