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

304 Actuarial Modelling of Claim Counts
Table 8.6
(Continued).
Age of policy Mature portfolio Young portfolio Old portfolio
47 2 % 05% 5%
48 2 % 05% 5%
49 2 % 05 % 10 %
50 2 % 05 % 10 %
Table 8.7 Relativities computed on the basis of the transient maximum accuracy criterion for the
former compulsory Belgian bonus-malus scale, and for different maturities of the portfolio.
Level l Mature Young Old Steady state
portfolio ¯r l portfolio ¯r l portfolio ¯r l distribution r l
22 2661 % 2536 % 2697 % 2715%
21 2344 % 2080 % 2426 % 2474%
20 2086 % 1738 % 2210 % 2291%
19 1874 % 1529 % 2030 % 2141%
18 1701 % 1382 % 1876 % 2014%
17 1561 % 1275 % 1744 % 1903%
16 1448 % 1197 % 1631 % 1803%
15 1356 % 1136 % 1529 % 1714%
14 1281 % 1097 % 1442 % 1631%
13 1219 % 1064 % 1365 % 1549%
12 1166 % 1035 % 1297 % 1472%
11 1118 % 1008 % 1238 % 1402%
10 1075% 982 % 1186 % 1340%
9 1038% 965 % 1131 % 1255%
8 1001% 942 % 1078 % 1173%
7 963% 914 % 1032 % 1114%
6 927% 888% 991 % 1067%
5 892% 863% 954 % 1028%
4 818% 844% 822% 826%
3 780% 792% 790% 802%
2 745% 754% 761% 778%
1 713% 725% 733% 755%
0 458% 505% 448% 451%
The linear premium scale is thus of the form
where
r lin
l
= E + CL A
l − EL
VL A
A
CL A =
+∑
a n
n=1
s∑
l=0
l ∑ k
w k
∫ +
0
p n
l
kdF − EL A E