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

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96 Actuarial Modelling of Claim Counts Number of policyholders 16000 15000 14000 13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 14331 15872 0.210 0.21 15147 0.20 0.19 0.178 0.18 0.17 0.166 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Large Middle Small 0.00 Large Middle Small Size of city Size of city Annual claim frequency Figure 2.13 Composition of Portfolio B with respect to Size of the city (left panel) and observed annual claim frequencies according to Size of the city (right panel). Nevertheless, several levels of the interaction between Age and Power can be grouped together. As already explained in Section 2.3.15, the option ‘Estimate’ of GENMOD can be used to assess the relevance of grouping the levels of the interaction Age–Power 2 by 2. The following groups have been defined: Group 1 Age > 30 and any power Group 2 Age 23–30 and any power as well as Age 18–22 and power > 110 kW Group 3 Age 18–22 and power < 110 kW The final model is shown in Table 2.10. The variance-covariance matrix of the estimated regression coefficients is ̂̂ = ⎛ ⎞ 0003428 −0000244 −0003022 −0003028 −0000441 −0000468 −0000244 0000679 0000012 0000006 −0000004 0000007 −0003022 0000012 0003350 0003064 −0000084 −0000050 ⎜ −0003028 0000006 0003064 0003436 −0000059 −0000045 ⎟ ⎝ −0000441 −0000004 −0000084 −0000059 0000938 0000511 ⎠ −0000468 0000007 −0000050 −0000045 0000511 0000964
Risk Classification 97 Number of policyholders 30000 29750 20000 14149 10000 1451 Annual claim frequency 0.19 0.187 0.183 0.18 0.17 0.156 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.00 66–110 kw 110 kw 66–110 kw 110 kw Power of car Power of car Figure 2.14 Composition of Portfolio B with respect to Power (left panel) and observed annual claim frequencies according to Power (right panel). Results of the Type 3 analysis are as follows: Source DF Chi-square Pr>Chi-sq Gender 1 650 00108 Age ∗ Power 2 17314
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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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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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