TABLE OF CONTENTS In insurance practice it often occurs that one has to set a premium for a group of insurance contracts for which there is some claim experience regarding the group itself, but a lot more on a larger group of contracts that are more or less related. The problem is then to set up an experience rating system to determine next year's premium, taking into account not only the individual experience with the group, but also the collective experience. There are two extreme positions possible. One is to charge the same premium to everyone, estimated by the overall mean X of the data. This makes sense if the portfolio is homogeneous, which means that all risk cells have identical mean claims. But if this is not the case, the 'good' risks will take their business elsewhere, leaving the insurer with only 'bad' risks. The other extreme is to charge to group j its own average claims X j as a premium. Such premiums are justified if the portfolio is heterogeneous, but they can only be applied if the claims experience with each group is large enough. As a compromise, already since the beginning of the 20th century one often asks a premium which is a weighted average of these two extremes:
| (7.1) |  |
The factor z j that expresses how 'credible' the individual experience of cell j is, is called the credibility factor; a premium such as (7.1) is called a credibility premium.
