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

Efficiency and Bonus Hunger 249
Table 5.13 Fit of the final model for the accident costs subject to bonus hunger in Portfolio C.
Variable Level Coeff Std error Wald 95 % conf limits Chi-sq Pr>Chi-sq
Intercept 58084 00402 57279 58889 2084738 < 00001
Ageph 18–24 02522 00661 01201 03843 1457 00001
Ageph > 24 0 0 0 0 . .
City Rural 00692 00274 00145 01240 639 00115
City Urban 0 0 0 0 . .
Agev 3–5 −01866 00394 −02653 −01078 2245 < 00001
Agev 6–10 −01582 00349 −02281 −00883 2051 < 00001
Agev 0–2 & > 10 0 0 0 0 .
Variable Level Coeff Std error Wald 95 % conf limits Chi-sq Pr>Chi-sq
Intercept 35269 00870 33529 37010 164272 < 00001
Ageph 18–24 −03077 01430 −05937 −00217 463 00314
Ageph > 60 06479 00852 04775 08183 5781 < 00001
Ageph 25–60 0 0 0 0 . .
Agev 0–2 −07126 01171 −09468 −04785 3704 < 00001
Agev 3–5 −03170 00666 −04503 −01837 2263 < 00001
Agev > 5 0 0 0 0 . .
BM level −00011 00006 −00022 00000 370 00546
Concerning the retention levels, we see that young drivers are more likely to defray only
relatively cheap accidents, whereas older drivers are ready to self-defray more expensive
accidents. The more recent the vehicle, the less accidents are self-defrayed. This may be due
to the fact that comprehensive coverage is often bought for new vehicles, so that claims are
filed to both third party liability and comprehensive. The effect of the level occupied in the
scale is as follows: policyholders occupying the middle of the scale are ready to defray more
expensive accidents than policyholders at the top or at the bottom of the scale.
5.4.2 Number of Claims and Number of Accidents
Let Mi
small be the number of small accidents caused by policyholder i. The number of
moderate claims filed by policyholder i is then given by
By equating the expectations, we get
EN small
i
= i =
Mi∑
small
N small
i
= ICA ik >RL i l i
=
+∑
k=0
+∑
k=0
k=1
PrM small
i
PrM small
i
= k
k∑
PrCA ij >RL i l i
j=1
= kk PrCA i1 >RL i l i
= PrCA i1 >RL i l i EM small
i