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

96 Actuarial Modelling of Claim Counts
Number of policyholders
16000
15000
14000
13000
12000
11000
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
14331
15872
0.210
0.21
15147
0.20
0.19
0.178
0.18
0.17
0.166
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Large Middle Small
0.00
Large Middle Small
Size of city
Size of city
Annual claim frequency
Figure 2.13 Composition of Portfolio B with respect to Size of the city (left panel) and observed
annual claim frequencies according to Size of the city (right panel).
Nevertheless, several levels of the interaction between Age and Power can be grouped
together. As already explained in Section 2.3.15, the option ‘Estimate’ of GENMOD can be
used to assess the relevance of grouping the levels of the interaction Age–Power 2 by 2. The
following groups have been defined:
Group 1 Age > 30 and any power
Group 2 Age 23–30 and any power as well as Age 18–22 and power > 110 kW
Group 3 Age 18–22 and power < 110 kW
The final model is shown in Table 2.10. The variance-covariance matrix of the estimated
regression coefficients is
̂̂
=
⎛
⎞
0003428 −0000244 −0003022 −0003028 −0000441 −0000468
−0000244 0000679 0000012 0000006 −0000004 0000007
−0003022 0000012 0003350 0003064 −0000084 −0000050
⎜ −0003028 0000006 0003064 0003436 −0000059 −0000045
⎟
⎝ −0000441 −0000004 −0000084 −0000059 0000938 0000511 ⎠
−0000468 0000007 −0000050 −0000045 0000511 0000964