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

58 Actuarial Modelling of Claim Counts
9000
8000
7000
8664
.160
.150
.140
.130
.120
.130
.157
Number of policyholders
6000
5000
4000
3000
5841
Annual claim frequency
.110
.100
.090
.080
.070
.060
.050
2000
.040
.030
1000
.020
.010
0
Rural Urban
District
.000
Rural Urban
District
Figure 2.4 Composition of Portfolio A with respect to District (left panel) and observed annual claim
frequencies according to District (right panel).
2.2.5 Interactions
So far, only the marginal effect of each observed covariate on the claim frequency has
been assessed. Besides these one-way analyses, it is also important to account for possible
interactions. Often Gender and Age interact, in the sense that the effect of Age on the average
claim frequency is different for males than for females. Typically, young male drivers are
more dangerous than young female drivers (but the higher risk associated with young male
drivers may be due to higher annual mileage, or to other risk factors correlated to the fact
of being a young male). Formally, two explanatory variables are said to interact when the
effect of one factor varies depending on the levels of the other factor. Multivariate models
allow for investigation into interaction effects.
This phenomenon can be seen from Figure 2.7. The observed annual claim frequency for
young males (ages 18–24) peaks at 23.8 %, whereas young females (ages 18–24) have an
observed annual claim frequency similar to males aged 25–30. Both genders become more
similar for categories 31–60 and over 60. We have thus detected an Age–Gender interaction
in Portfolio A.
Note that standard regression models do not automatically account for interaction (in
contrast to correlations between covariates, for which the estimated regression coefficients