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

198 Actuarial Modelling of Claim Counts
Table 4.13 Numerical characteristics for the systems −1/top,
−1/ + 2 and −1/ + 3 with a severity c = 1 and Portofolio A.
−1/top
Level l
Relativity r exp
l
without a priori
ratemaking
Relativity r exp
l
with a priori
ratemaking
5 1613 % 1541%
4 1480 % 1423%
3 1371 % 1329%
2 1281 % 1252%
1 1204 % 1187%
0 690% 723%
−1/ + 2
Level l
Relativity r exp
l
without a priori
ratemaking
Relativity r exp
l
with a priori
ratemaking
5 2534 % 2293%
4 2044 % 1898%
3 1834 % 1726%
2 1328 % 1300%
1 1249 % 1234%
0 716% 758%
−1/ + 3
Level l
Relativity r exp
l
without a priori
ratemaking
Relativity r exp
l
with a priori
ratemaking
5 2093 % 1947%
4 1878 % 1763%
3 1372 % 1334%
2 1283 % 1259%
1 1207 % 1194%
0 693% 732%
Tables 4.14, 4.15 and 4.16 respectively for the −1/top, −1/ + 2 and −1/ + 3 systems. The
exponential relativities have been computed for a severity coefficient ranging from 0 to 5.
The limit value of c = 0 provides the same result as with the quadratic loss function. We
observe in Table 4.14 that an increasing value of c leads to less dispersed relativities. The
maximal penalty decreases as c increases: keeping financial balance, increasing c tends to
soften a posteriori corrections.