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

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60 Actuarial Modelling of Claim Counts Number of policyholders 0 Not split Split 11000 .220 10568 .210 10000 .200 .190 9000 .180 .170 8000 .160 .000 .150 7000 .140 .130 6000 .120 .110 5000 .100 4000 3000 2000 1000 3957 .090 .080 .070 .060 .050 .040 .030 .020 .010 Premium split Annual claim frequency .211 .124 Not split Split Premium split Figure 2.6 Composition of Portfolio A with respect to Split (left panel) and observed annual claim frequencies according to Split (right panel). Example 2.1 Assume that living in rural or urban areas (observed covariate District) does not influence claim occurrences but the driving experience (hidden characteristic) does. Specifically, let us assume that PrN ≥ 1inexperienced, rural = PrN ≥ 1inexperienced, urban = PrN ≥ 1inexperienced = 015 PrN ≥ 1experienced, rural = PrN ≥ 1experienced, urban = PrN ≥ 1experienced = 005 The portfolio comprises 50 % inexperienced drivers, but and Prinexperiencedurban = 1 − Prexperiencedurban = 09 Prinexperiencedrural = 1 − Prexperiencedrural = 01
Risk Classification 61 Number of policyholders 5000 .240 .230 .220 4286 .210 .200 4000 .190 .180 .170 .160 2972 .150 3000 .140 .130 2436 .120 .110 2000 .100 1714 .090 1494 .080 .070 .060 1000 .050 801 606 .040 .030 196 .020 .010 0 .000 F 18–24 F 25–30 F 31–60 F >60 M 18–24 M 25–30 Interaction Age–Gender M 31–60 M >60 Annual claim frequency .165 F 18–24 .140 F 25–30 .127 F 31–60 .112 F >60 .238 M 18–24 .164 M 25–30 Interaction Age–Gender .120 M 31–60 .107 M >60 Figure 2.7 Composition of Portfolio A with respect to the Age–Gender interaction (left panel) and observed annual claim frequencies according to the Age–Gender interaction (right panel). In other words, there is a majority of experienced drivers in rural areas (90 %) whereas in urban areas, the majority of drivers are inexperienced. Clearly, whereas PrN ≥ 1urban = PrN ≥ 1inexperienced, urban Prinexperiencedurban + PrN ≥ 1experienced, urban Prexperiencedurban = 014 PrN ≥ 1rural = PrN ≥ 1inexperienced, rural Prinexperiencedrural + PrN ≥ 1experienced, rural Prexperiencedrural = 006 Even if District does not influence the number of claims once the driving experience has been accounted for, unconditionally there is some dependence between District and the number of claims filed by policyholders. The univariate analysis will detect a rural/urban effect, but the latter should disappear in the multivariate analysis (taking experience and the variable District into account). Therefore, we cannot say after a marginal analysis that living in an urban area causes an increase in the average number of claims: both variables are related to driving experience.
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Actuarial Modelling of Claim Counts
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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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Part III Advances in Experience Rat
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8 Transient Maximum Accuracy Criter
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Transient Maximum Accuracy Criterio
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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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