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

Efficiency and Bonus Hunger 243
Loimaranta efficiency
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.7
0.6
Scale –1/top
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Claims frequency
Scale –1/+2
Loimaranta efficiency
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Claims frequency
Loimaranta efficiency
0.48
0.46
0.44
0.42
0.40
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Scale –1/+3
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Claims frequency
Figure 5.2 Loimaranta efficiency as a function of the annual expected claim frequencies for the three
bonus-malus systems and Portfolio A.