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

154 Actuarial Modelling of Claim Counts
Table 3.15 Values of the a posteriori corrections obtained from (3.17) for
different combinations of observed periods T i and number of past claims k • for a
bad driver (expected annual claim frequency equal to 28.40 %) from Portfolio A,
with c = 1.
T i
Number of claims k •
0 1 2 3 4 5
1 80.9 % 1482 % 2154 % 282.7 % 350.0 % 417.2 %
2 67.9 % 1244 % 1808 % 237.3 % 293.8 % 350.2 %
3 58.6 % 1072 % 1558 % 204.5 % 253.1 % 301.8 %
4 51.5 % 942 % 1369 % 179.6 % 222.4 % 265.1 %
5 45.9 % 840 % 1221 % 160.2 % 198.3 % 236.4 %
6 41.4 % 758 % 1102 % 144.5 % 178.9 % 213.3 %
7 37.7 % 691 % 1004 % 131.7 % 163.0 % 194.3 %
8 34.7 % 634% 922 % 120.9 % 149.7 % 178.4 %
9 32.0 % 586% 852 % 111.8 % 138.4 % 165.0 %
10 29.8 % 545% 792 % 103.9 % 128.7 % 153.4 %
Table 3.16 Values of the a posteriori corrections obtained from (3.17) for different
combinations of observed periods T i and number of past claims k • for a good driver
(expected annual claim frequency equal to 9.28 %) from Portfolio A, with c = 5.
T i
Number of claims k •
0 1 2 3 4 5
1 93.3 % 165.9 % 238.5 % 311.1 % 383.8 % 456.4 %
2 87.4 % 155.4 % 223.4 % 291.4 % 359.4 % 427.4 %
3 82.2 % 146.1 % 210.1 % 274.0 % 338.0 % 401.9 %
4 77.6 % 137.9 % 198.3 % 258.6 % 318.9 % 379.3 %
5 73.5 % 130.6 % 187.7 % 244.9 % 302.0 % 359.1 %
6 69.8 % 124.0 % 178.3 % 232.5 % 286.7 % 340.9 %
7 66.5 % 118.1 % 169.7 % 221.3 % 272.9 % 324.6 %
8 63.4 % 112.7 % 161.9 % 211.2 % 260.4 % 309.7 %
9 60.7 % 107.8 % 154.8 % 201.9 % 249.0 % 296.1 %
10 58.1 % 103.2 % 148.4 % 193.5 % 238.6 % 283.7 %
If we compare the a posteriori corrections for the different types of drivers, we see
that the discounts increase with the average annual claim frequency, as was the case with
the quadratic loss function. Also, the penalties appear to decrease with the average annual
claim frequencies. The fact that a priori bad drivers need a greater premium reduction
when no claim is filed to the insurance company thus remains with exponential loss
functions.