A Theoretical Study of the No-Claim Bonus Problem

The no-claim bonus problem has given rise to a considerable amount of discussion throughout the whole world. There is quite a difference of opinion among the actuaries and other experts concerned in this field and several exchanges of view have taken place the last few years. The ASTIN section of the Permanent Committee has been well aware of this fact and it has devoted one Colloquium to this subject and discussed it at others.In 1959 the major part of the La Baule meeting was dedicated to this subject and attention was focussed on this problem once again at Rattvik in 1961. Nevertheless controversies on this subject still continue. Almost every conference where the bonus problem is discussed is marked by a widespread difference of opinion.As is well known, the claim frequencies under insurance policies show a considerable heterogeneity, especially in the early years. It is not possible to get homogeneous sub-groups by means of a continuous subdivision; what may be gained in homogeneity, is lost in credibility. It seems therefore that a subsequent adjustment of premiums according to the past claim record may well be a suitable way of obtaining a fair premium.Those who are in favour of a rating procedure granting a bonus at a careful driver will stress that criticism is useless as long as no better solution is available, whereas actuaries who reject such a rating system argue that the unfairness of a flat rate is not at all eliminated by means of a bonus.