Some extensions of the Bühlmann-Straub credibility formulae

The paper presents some extensions of the Bühlmann-Straub credibility model. In the sequel we describe covariance structures leading to credibility formulae of the updating type, where the new credibility adjusted premium can be computed as a weighted average of the premium quoted in the previous period and the claims in this period. The credibility formula of the updating type is introduced for a wider class of models from the credibility theory, where the risk parameter does not remain the same ever time, and its properties are studied. Also, the expected values (the means) and credibility formulae of the updating type are emphasized. Finally we establish an application which shows that these formulae are attractive from practical point of view, because easy recursive formulae for the computation of the credibility weights (factors) from the Bühlmann-Straub model, can be derived.