Geometrical credibility

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Abstract
The paper presents a self-contained survey of the most interesting recent results in credibility theory of Bühlmann, Straub, Jewell, Hachemeister and Taylor, using as framework the real Hilbert space of random variables with finite second order moments defined on a fixed probability space. It appears that only those elements of Hilbert space having an obvious counterpart in the usual euclidean space are necessary for the development of the theory. With that fact in mind, it was possible to present an elementary treatment necessitating no previous knowledge of Hilbert space theory. The discovery of the geometrical character of credibility theory is not new. Hilbert space techniques are used in Gerber & Jones (1975). Thus, little of the present paper can be regarded as really original. However, by the absorption of the great existing models, developed by an uniform method, it is hoped that these notes are of interest, at least for the newcomer to the subject.

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