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...

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...

The management of any activity need to know, first of all, the goals to be achieved and, on other hand, the necessary resources to fulfill the objectives. The budget is short-term forecasting in monetary or natural units, all operations of an enterprise, for programming and control of the...

It is an original paper, which shows how the hierarchical model with two levels, can be used to determine the linear non-homogeneous credibility premiums at the sector level and at the contract level. The fact that it is based on complicated mathematics, involving conditional expectations,...

In this article we give the mathematical theory of some credibility models. The first section describes the original credibility model of Bühlmann and we derive the best linearized credibility estimator for this model. His original model, involving only one contract, contains the basics of all...

Is an original paper, which describes techniques for estimating premiums for risks, containing a fraction (a part) of the variance of the risk as a loading on the net risk premium.

The paper presents the mathematical theory of some credibility models, involving complicated properties of conditional expectations and conditional covariance. The fact that is based on complicated mathematics will give more insight and understanding of the theoretical aspects and will point the...

An original paper which suggests a way of thinking for semilinear credibility theory develpment, founded on analysis of the functions of the observable random variables. This line of thought fits perfectly within the framework of the greatest accuracy credibility theory.