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

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242 Actuarial Modelling of Claim Counts Figure 5.2 displays the Loimaranta efficiency as a function of the annual expected claim frequencies for the three bonus-malus systems. We see that the efficiency first increases and then decreases, reaching its maximum value at about 15 % for the −1/top bonus-malus system, at about 30 % for the −1/+2 bonus-malus system, and at about 25 % for the −1/+3 bonus-malus system. 5.3.2 De Pril Efficiency Definition Loimaranta efficiency is an asymptotic concept that does not depend on the level presently occupied in the scale. De Pril efficiency is a transient concept that explicitly considers time value of money. Let v
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.
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Contents Foreword Preface Notation
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Contents vii 2.4 Overdispersion 79
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Contents ix 4.2.3 Trajectory 170 4.
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Contents xi 7.4 Numerical Illustrat
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Part I Modelling Claim Counts Actua
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3 Credibility Models for Claim Coun
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Credibility Models for Claim Counts
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8 Transient Maximum Accuracy Criter
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Bibliography Albrecht, P. (1983a).
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Bibliography 347 Daengdej, J., Luko
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Bibliography 349 Greenwood, M., & Y
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Bibliography 351 Norberg, R. (1976)
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Bibliography 353 Walhin, J.-F., & P
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