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

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236 Actuarial Modelling of Claim Counts Table 5.5 Results of the LogNormal regression analysis for the claim costs recorded in Portfolio C. Variable Level Coeff Std error Wald 95 % conf limit t-value Pr >t Intercept 61223 00268 60702 61744 23038 60 01781 00312 01169 02392 571 Chi-sq Ageph 2 4058 < .0001 City 1 770 0.0055 Agev 3 3820 < .0001 All the three remaining variables are statistically significant, and must be kept in the model. 5.2.6 Resulting Price List for Portfolio C Formula for the Pure Premium Let freq be the vector of the regression coefficient for the claim frequencies, that is, the expected annual number of standard claims is exp freq 0 + ∑ p j=1 freq j x ij . Similarly, let cost be the regression coefficient for the moderate claim sizes. We retain here the LogNormal modelling for the moderate claim sizes, so that the expected moderate claim amount is exp cost 0 + ∑ p j=1 cost j x ij + 2 /2. Neglecting the large claims, the pure premium for policyholder i is given by ⎡ ⎤ Ni∑ small ( p∑ ( E ⎣ C ik ⎦ = EN small i EC i1 = exp freq 0 + cost 0 + freq ) ) j + cost j xij + 2 2 k=1 If all the components of x i are binary, we then get a multiplicative price list. The total premium is then obtained by adding the expected cost of the large losses, i.e. EN large i EL i1 . j=1
Efficiency and Bonus Hunger 237 We still need to estimate freq to be able to compute the pure premium for the different categories of policyholders in Portfolio C. Risk Classification for Claim Frequencies Here we follow the method described in Chapter 2 for analysing the observed claim numbers. A Poisson regression is first performed on the claim frequencies of Portfolio C. This leads to the results of Table 5.6. Only the Use of the vehicle has been removed from the model (p-value of 3448 %). The levels 0–2, 6–10 and > 10 of the variable Agev are grouped together. The log-likelihood of the final model is equal to −61 5639 and the Type 3 analysis is presented in the following table: Source DF Chi-square Pr>Chi-sq Ageph 3 89266
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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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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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