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

3
Credibility Models for Claim
Counts
3.1 Introduction
3.1.1 From Risk Classification to Experience Rating
We have seen in Chapter 2 how to partition a heterogeneous portfolio into more homogeneous
classes with all policyholders belonging to the same class paying the same premium.
However, tariff cells are still quite heterogeneous despite the use of many a priori variables.
The expected claim frequency for the tariff cell is designed to reflect the average experience
of the entire group. If the experience of a policy is consistently better (or worse) than the
average experience of the group, the insurance company may consider adapting the amount
of premium to be charged for this policy. Of course, this requires a model which can separate
random variation from signal in the historical data to indicate whether this policy is of better
(or worse) quality compared to the group average.
It is reasonable to believe that the hidden features (unobserved risk characteristics that
have been modelled by a random effect in the mixed Poisson regression model) are revealed
by the number of claims reported by the policyholders over the successive insurance periods.
Hence the adjustment of the premium based on the individual claims experience in order
to restore fairness among policyholders. The allowance for the history of the policyholder
in a rating model thus derives from interpretation of serial correlation for longitudinal data
resulting from hidden features in the risk distribution.
3.1.2 Credibility Theory
Credibility theory is the art of combining different collections of data to obtain an accurate
overall estimate. It provides actuaries with techniques to determine insurance premiums for
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,