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

Risk Classification 61
Number of policyholders
5000 .240
.230
.220
4286
.210
.200
4000
.190
.180
.170
.160
2972
.150
3000
.140
.130
2436
.120
.110
2000
.100
1714
.090
1494
.080
.070
.060
1000 .050
801
606
.040
.030
196
.020
.010
0
.000
F
18–24
F
25–30
F
31–60
F
>60
M
18–24
M
25–30
Interaction Age–Gender
M
31–60
M
>60
Annual claim frequency
.165
F
18–24
.140
F
25–30
.127
F
31–60
.112
F
>60
.238
M
18–24
.164
M
25–30
Interaction Age–Gender
.120
M
31–60
.107
M
>60
Figure 2.7 Composition of Portfolio A with respect to the Age–Gender interaction (left panel) and
observed annual claim frequencies according to the Age–Gender interaction (right panel).
In other words, there is a majority of experienced drivers in rural areas (90 %) whereas in
urban areas, the majority of drivers are inexperienced.
Clearly,
whereas
PrN ≥ 1urban = PrN ≥ 1inexperienced, urban Prinexperiencedurban
+ PrN ≥ 1experienced, urban Prexperiencedurban
= 014
PrN ≥ 1rural = PrN ≥ 1inexperienced, rural Prinexperiencedrural
+ PrN ≥ 1experienced, rural Prexperiencedrural
= 006
Even if District does not influence the number of claims once the driving experience has been
accounted for, unconditionally there is some dependence between District and the number
of claims filed by policyholders. The univariate analysis will detect a rural/urban effect, but
the latter should disappear in the multivariate analysis (taking experience and the variable
District into account). Therefore, we cannot say after a marginal analysis that living in an
urban area causes an increase in the average number of claims: both variables are related to
driving experience.