Combining Credibility and GLM for Rating of Multi-Level Factors

A multi-level factor (MLF) is a rating factor with a large number of levels, each of which we want to rate separately even though many of them do not have a sufficient amount of data. Examples include Car model, Geographic Zone and Company (in experience rating).

Rating of MLFs is a standard situation for employing credibility theory. Traditional credibility theory models MLFs as random effects, but does not treat the situation where there are also ordinary rating factors (like Sex and Age class) alongside with the MLF. The aim of this paper is to show how such a situation can be handled by combining credibility theory and GLM. The method can be seen as an extension of the classical Buhlmann-Straub approach.

The method is presented via an example of experience rating in bus insurance, while the theory and more general results are given in Ohlsson and Johannson(2003).