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

254 Actuarial Modelling of Claim Counts
Note also that this approach requires knowledge of the uncensored distribution for claim
costs and claim counts, which is usually not available in practice. The probability density
function f corresponds to the cost of an accident (and not to the cost of a claim), and the
distribution of the number of accidents is actually needed (not only the distribution of the
number of claims that has been studied in the preceding chapters). Hence, the methodology
described in Sections 5.4.1–5.4.2 has first to be applied to obtain the uncensored accident
distribution.
Application of the Lemaire Algorithm to Portfolio C
The Lemaire algorithm can be applied with the distribution obtained for the cost of accidents
(i.e. with the help of the LogNormal model with corrected regression coefficients) after
having transformed the claim frequencies for Portfolio C into the accident frequencies.
Let us consider the −1/+2 bonus-malus scale, with relativities 62.4 % for level 0, 130.2 %
for level 1, 142.9 % for level 2, 207.7 % for level 3, 241.4 % for level 4, and 309.1 % for
level 5. We consider here a discount rate of 4 %.
Let us consider an individual aged between 25 and 60, living in a rural area, and driving a
vehicle between 6 and 10 years old. His claim frequency is 18.46 %. His accident frequency
is 21.29 %. The base pure premium is taken as the product of the claim frequency times the
grand mean of all the claim sizes (large and moderate ones), that is, 01846 × E 181063.
The optimal retentions are as follows:
Level l
Optimal retention
0 E57475
1 E105039
2 E134116
3 E176077
4 E126069
5 E69370
We see that this policyholder should defray accidents with a cost up to E 1760.77 if he
occupied level 3.
Let us now consider an individual aged over 60, living in a urban area, and driving a
vehicle between 3 and 5 years old. His claim frequency is 17.41 %. His accident frequency
is 21.37 %. The base premium amounts to 01741 × E 181063. The optimal retentions are
as follows:
Level l
Optimal retention
0 E53989
1 E98774
2 E126284
3 E166053
4 E118990
5 E65534
The optimal retentions are now slightly smaller than before.