Bonus-Malus Systems in Automobile Insurance by Jean Lemaire

By Jean Lemaire

Most insurers all over the world have brought a few type of merit-rating in vehicle 3rd celebration legal responsibility assurance. Such platforms, penalizing at-fault injuries by means of top class surcharges and worthwhile claim-free years by means of rate reductions, are referred to as bonus-malus structures (BMS) in Europe and Asia. With the present deregulation developments that hindrance such a lot assurance markets all over the world, many businesses might want to enhance their very own BMS. the most aim of the ebook is to supply them versions to layout BMS that meet their targets.
half I of the publication includes an total presentation of the professionals and cons of merit-rating, a case examine and a overview of the several chance distributions that may be used to version the variety of claims in an vehicle portfolio. partially II, 30 structures from 22 diversified nations, are evaluated and ranked in accordance with their `toughness' in the direction of policyholders. 4 instruments are created to judge that longevity and supply a tentative type of all structures. Then, issue research is used to mixture and summarize the knowledge, and supply a last rating of all platforms. half III is an up to date evaluate of the entire chance versions which were proposed for the layout of an optimum BMS. the appliance of those versions may allow the reader to plot the procedure that's very best to the habit of the policyholders of his personal assurance corporation. ultimately, half IV analyses an alternative choice to BMS; the advent of a coverage with a deductible.

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1011, and multiplying them by the sample size 106,974, lead to the fitted theoretical frequencies presented in column 3 of table 3-2. 26 MODELS FOR CLAIM NUMBER DISTRIBUTIONS Table 3-2. 991). There is not enough probability mass in the right tail of the Poisson distribution. The Poisson model cannot be applied to this automobile portfolio. The homogeneity hypothesis is not compatible with statistical analysis. We need a distribution whose variance exceeds its mean. This result already proves that the introduction of a BMS in automobile insurance is justified.

The skewness coefficient of a mixed Poisson distribution is where C=2 for the negative binomial and C=3 for the Poisson-inverse MODELS FOR CLAIM NUMBER DISTRIBUTIONS 40 Gaussian. The Poisson-inverse Gaussian is thus more skewed than the negative binomial and has a somewhat thicker right tail. Table 3-8 shows that, in practice, differences are insignificant. The skewness coefficient cannot be used as a tie-breaker between the negative binomial and the Poisson-inverse Gaussian. Table 3-8. 4534 Conclusion.

Such a system is determined by three elements: * The premium scale * The initial class C; , and o b = (b" ... ,b s ), DEFINITION OF A BONUS-MALUS SYSTEM * 7 The transition rules -the rules that determine the transfer from one class to another when the number of claims is known. These rules can be introduced in the form of transformations Tk , such that Tk(i) = j ifthe policy is transferred from class C i into class Cj when k claims have been reported. Tk can be written in the form of a matrix where tij(k) = 1 if Tk(i) = j and 0 otherwise.

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