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

Risk Classification 111
Table 2.16
A priori risk classification for Portfolio B (Poisson-LogNormal regression model).
Age–Power Size of the city Gender Annual
claim freq. (%)
Group 1 Group 2 Group 3 Large Middle Small Female Male
Weights
(%)
No No Yes No No Yes No Yes 2950 082
No No Yes No No Yes Yes No 2759 043
No No Yes No Yes No No Yes 3173 063
No No Yes No Yes No Yes No 2968 037
No No Yes Yes No No No Yes 3833 044
No No Yes Yes No No Yes No 3586 031
No Yes No No No Yes No Yes 1960 788
No Yes No No No Yes Yes No 1833 464
No Yes No No Yes No No Yes 2108 832
No Yes No No Yes No Yes No 1972 466
No Yes No Yes No No No Yes 2547 689
No Yes No Yes No No Yes No 2382 399
Yes No No No No Yes No Yes 1519 1259
Yes No No No No Yes Yes No 1420 702
Yes No No No Yes No No Yes 1634 1381
Yes No No No Yes No Yes No 1528 724
Yes No No Yes No No No Yes 1974 1268
Yes No No Yes No No Yes No 1846 730
2950 %
{ exp−00669 = 094 if the policyholder is a female driver
×
1
otherwise
⎧
exp−06640 = 051 if the policyholder belongs to Group 1 with respect to
⎪⎨
the combined variable Age ∗ Power
× exp−04089 = 066 if the policyholder belongs to Group 2 with respect to
the combined variable Age ⎪⎩
∗ Power
1
otherwise
⎧
⎨ exp02620 = 130 if the policyholder resides in a large city
× exp00731 = 108 if the policyholder resides in a middle-sized city
⎩
1
otherwise
2.10 Further Reading and Bibliographic Notes
2.10.1 Generalized Linear Models
After decades dominated by statistically unsophisticated models, it is now common practice
since Mc Cullagh & Nelder (1989) and Brockman & Wright (1992) to achieve a priori
classification with the help of generalized linear models (GLMs). They are so called because
they generalize the classical linear models based on the Normal distribution.