In this paper, we give the mathematical theory of the credibility model incorporating risk volumes. In the simple model of Section 1, we assumed that the risk volume was the same for all years. Often, in particular in reinsurance, one wants to allow for varying risk volumes, and for that purpose...

The idea of considering regression credibility models originated from Hachemeister. Just like in the case of classical credibility models, we will obtain a credibility solution in the form of a linear combination of the individual estimate (based on the data of a particular state) and the...

In many cases there is more than one risk factor dividing the portfolio in different subclasses or sectors. One could for instance consider a first subdivision in industrial fire insurance and fire insurance covering private households. Other risk factors may be used to further classify the...

This is an original paper, which analyses some practical insurance problems of non-life insurance, with applications in the actuarial calculations that can be solved by means of credibility theory. Examples of the credibility results for the linearized premiums, as other applications for the...

In this paper, we give the mathematical theory of the hierarchical credibility model, which consists of a portfolio of contracts, for homogeneous linear credibility estimators. The theorem obtained (see section 1) shows that this happens to give the optimal unbiased homogeneous liniarized...