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

270 Actuarial Modelling of Claim Counts
Table 6.3 Evolution of relativities and pure premiums (taking the average cost of a claim with
material damage only (mat) as the monetary unit, and assuming that claims with bodily injuries (bod)
are on average ten times more expensive) if a single claim with material damage only has been reported
during the first year.
Time Good driver Bad driver
Relativity
mat
Relativity
bod
Pure
premium
Relativity
mat
Relativity
bod
Pure
premium
1 171.6 % 152.0 % 29.0 % 150.7 % 134.9 % 77.0 %
2 160.3 % 142.8 % 27.2 % 127.3 % 115.7 % 65.6 %
3 150.4 % 134.7 % 25.6 % 110.1 % 101.6 % 57.2 %
4 141.7 % 127.6 % 24.1 % 97.0 % 90.7 % 50.8 %
5 133.9 % 121.2 % 22.9 % 86.7 % 82.2 % 45.7 %
6 126.9 % 115.5 % 21.7 % 78.3 % 75.2 % 41.6 %
7 120.6 % 110.3 % 20.7 % 71.4 % 69.4 % 38.1 %
8 114.9 % 105.7 % 19.8 % 65.6 % 64.6 % 35.3 %
9 109.7 % 101.4 % 18.9 % 60.7 % 60.4 % 32.8 %
10 105.0 % 97.5 % 18.2 % 56.5 % 56.8 % 30.7 %
Table 6.4 Evolution of relativities and pure premiums (taking the average cost of a claim with
material damage only (mat) as the monetary unit, and assuming that claims with bodily injuries (bod)
are on average ten times more expensive) if a single claim with bodily injuries has been reported
during the first year.
Time Good driver Bad driver
Relativity
mat
Relativity
bod
Pure
premium
Relativity
mat
Relativity
bod
Pure
premium
1 150.7 % 201.9 % 32.1 % 131.7 % 185.5 % 87.3 %
2 140.5 % 193.1 % 30.4 % 110.4 % 166.8 % 76.6 %
3 131.5 % 185.4 % 28.9 % 94.8 % 152.9 % 68.6 %
4 123.5 % 178.5 % 27.6 % 82.9 % 142.0 % 62.4 %
5 116.5 % 172.3 % 26.4 % 73.6 % 133.2 % 57.5 %
6 101.1 % 166.7 % 25.3 % 66.0 % 125.8 % 53.5 %
7 104.4 % 161.7 % 24.3 % 59.8 % 119.6 % 50.1 %
8 99.2 % 157.0 % 23.5 % 54.6 % 114.3 % 47.3 %
9 94.5 % 152.8 % 22.7 % 50.2 % 109.6 % 44.8 %
10 90.2 % 148.9 % 21.9 % 46.4 % 105.5 % 42.6 %
6.3 Multi-Event Bonus-Malus Scales
6.3.1 Types of Claims
Here we adopt the same assumptions as in Chapter 4. Let us pick a policyholder at random
from the portfolio and let us denote as N the number of claims reported during the year.
Furthermore, let be the (unknown) a priori expected claim frequency, with Pr = k = w k .