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

Risk Classification 59
13000
12000
12745
.150
.140
.147
.143
11000
.130
Number of policyholders
10000
9000
8000
7000
6000
5000
4000
3000
2000
1760
Annual claim frequency
.120
.110
.100
.090
.080
.070
.060
.050
.040
.030
.020
1000
.010
0
Private Professional
Use of car
.000
Private Professional
Use of car
Figure 2.5 Composition of Portfolio A with respect to Use (left panel) and observed annual claim
frequencies according to Use (right panel).
are adjusted). The reason is as follows: interactions cannot be rendered by linear combinations
of the covariates. To account for interactions, nonlinear functions of the covariates (products)
are needed, as explained in Example 2.3 below. In ANOVA terminology, one would speak
of interaction when the effects are not just additive. The actuary needs to identify the existing
interactions at the preliminary exploratory stage, and then define new ratemaking factors
combining the levels of the two interacting variables. Inserting these new factors in the
regression model then allows us to account for interaction.
2.2.6 True Versus Apparent Dependence
The descriptive analysis conducted so far suggests that some observed characteristics may
influence the number of claims reported to the company. It is nevertheless important to
realize the kind of relationship just evidenced: the actuary has to keep in mind that he
has not established any causal relationship so far, but only that some correlations seem
to exist between the rating factors and the number of claims. Such correlations may have
been produced by a causal relationship, but could also result from confounding effects. The
following simple example illustrates this situation.