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

Bonus-Malus Scales 201
Table 4.17 Transition rules of the Belgian bonus-malus system with fictitious levels accounting for
the special bonus rule.
Class
Class after k accidents
k = 0 1 2 3 4 5
22 211 22 22 22 22 22
21.0 201 22 22 22 22 22
21.1 202 22 22 22 22 22
20.0 191 22 22 22 22 22
20.1 192 22 22 22 22 22
20.2 193 22 22 22 22 22
19.0 181 22 22 22 22 22
19.1 182 22 22 22 22 22
19.2 183 22 22 22 22 22
19.3 14 22 22 22 22 22
18.0 17 22 22 22 22 22
18.1 172 22 22 22 22 22
18.2 173 22 22 22 22 22
18.3 14 22 22 22 22 22
17 16 210 22 22 22 22
17.2 163 210 22 22 22 22
17.3 14 210 22 22 22 22
16 15 200 22 22 22 22
16.3 14 200 22 22 22 22
15 14 190 22 22 22 22
14 13 180 22 22 22 22
13 12 17 22 22 22 22
12 11 16 210 22 22 22
11 10 15 200 22 22 22
10 9 14 190 22 22 22
9 8 13 180 22 22 22
8 7 12 17 22 22 22
7 6 11 16 210 22 22
6 5 10 15 200 22 22
5 4 9 14 190 22 22
4 3 8 13 180 22 22
3 2 7 12 17 22 22
2 1 6 11 16 210 22
1 0 5 10 15 200 22
0 0 4 9 14 190 22
Note that it is easily seen that
n j
∑ PrL = ji
r j = ∑ nj
i=1 i=1 PrL = jir ji
where the r ji s represent the non-constrained solution of the minimization of [ − r L 2] .