Actuarial Modelling of Claim Counts Risk Classification, Credibility ...

4
Bonus-Malus Scales
4.1 Introduction
4.1.1 From Credibility to Bonus-Malus Scales
One of the main tasks of the actuary is to design a tariff structure that will fairly distribute the
burden of claims among policyholders. To this end, he often has to partition all policies into
risk classes with all policyholders belonging to the same class paying the same premium. It
is convenient to achieve a priori classification by resorting to generalized linear models (e.g.
Poisson regression for claim counts), as explained in Chapter 2. However, many important
factors cannot be taken into account at this stage. Consequently, risk classes are still quite
heterogeneous despite the use of many a priori variables.
Rating systems penalizing insureds responsible for one or more accidents by premium
surcharges (or maluses), and rewarding claim-free policyholders by awarding them
discounts (or bonuses) are now in force in many developed countries. Besides encouraging
policyholders to drive carefully (i.e. counteracting moral hazard), they aim to better
assess individual risks. The amount of premium is adjusted each year on the basis of
the individual claims experience using techniques from credibility theory, as shown in
Chapter 3.
However, credibility formulas are difficult to implement in practice, because of their
mathematical complexity (complexity refers here to the sphere of commercial relations,
where customers are often reluctant in using mechanisms that they consider to be complex,
especially in connection with insurance products). For this reason, bonus-malus scales have
been proposed by insurance companies. Such scales have to be seen as commercial versions
of credibility formulas. The typical customer can figure out what the premium will be for
any given claims history.
Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems
S. Pitrebois and J.-F. Walhin © 2007 John Wiley & Sons, Ltd
M. Denuit, X. Maréchal,