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

Bonus-Malus Scales 207
∑16
j=13
r j j =
∑16
j=13
r ′ j ≥ 169 %
r ′ j ≤ 194 %
r ′ j j
j = 1316
j = 1316
And we obtain r ′ 13 = 1798 % and r ′ 14 = r ′ 15 = r ′ 16
= 1878 %. The value of Q is now 041135.
4.7.5 Linear Relativities for the Belgian Scale
We shall now demonstrate how to get linear relativities for the Belgian scale. In addition to
the constraint of building a linear scale, we add a new constraint: the artificial states must
have the same relativity. The minimization problem then becomes :
[ ] ]
min E − r lin
L 2 = min E
[ − − L 2
Table 4.23 Relativities r l and rl
lin for the Belgian
bonus-malus system, taking into account the special
bonus rule and computed on the basis of Portfolio A.
Level l
Relativities
General scale Linear scale
22 2843 % 2674%
21 2589 % 2574%
20 2389 % 2475%
19 2225 % 2376%
18 1994 % 2276%
17 1942 % 2177%
16 1869 % 2077%
15 1791 % 1978%
14 1924 % 1879%
13 1798 % 1779%
12 1684 % 1680%
11 1583 % 1580%
10 1495 % 1481%
9 1386 % 1382%
8 1283 % 1282%
7 1207 % 1183%
6 1147 % 1083%
5 1096% 984%
4 870% 885%
3 841% 785%
2 813% 686%
1 786% 586%
0 462% 487%