By Jean Lemaire
Most insurers worldwide have brought a few type of merit-rating in motor vehicle 3rd social gathering legal responsibility assurance. Such structures, penalizing at-fault injuries via top rate surcharges and profitable claim-free years by means of discount rates, are known as bonus-malus structures (BMS) in Europe and Asia. With the present deregulation developments that main issue so much coverage markets around the globe, many businesses might want to boost their very own BMS. the most target of the publication is to supply them types to layout BMS that meet their goals.
half I of the ebook comprises an total presentation of the professionals and cons of merit-rating, a case research and a assessment of different likelihood distributions that may be used to version the variety of claims in an vehicle portfolio. partly II, 30 structures from 22 assorted nations, are evaluated and ranked in keeping with their `toughness' in the direction of policyholders. 4 instruments are created to judge that durability and supply a tentative class of all platforms. Then, issue research is used to combination and summarize the knowledge, and supply a last rating of all platforms. half III is an updated assessment of the entire likelihood types which were proposed for the layout of an optimum BMS. the applying of those types could allow the reader to plot the process that's excellent to the habit of the policyholders of his personal coverage corporation. ultimately, half IV analyses an alternative choice to BMS; the creation of a coverage with a deductible.
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Extra resources for Bonus-Malus Systems in Automobile Insurance
Usually, the data are first transformed into a uniform distribution, and goodness-of-fit tests for uniformity are applied to the transformed data; 6. Tests based on the third and fourth sample moments; and 7. Special-purpose tests, designed to test a specific distribution only. A wide variety of tests for Poisson data are described in Cox and Lewis (1966). Most of the alternative tests are designed for continuous distributions and cannot be used for discrete distributions such as claim counts. Several of the tests that apply to discrete distributions have been applied to the different models presented in this part.
They can be classified as follows: 1. Chi-square-type tests; 2. Tests based on the deviation between the empirical distribution function (EDF) and the theoretical distribution function (TDF). The best-known examples are the Kolmogorov-Smirnov test, based on the maximum deviation between the EDF and TDF, and the Cramer-von Mises and Anderson-Darling tests. based on quadratic deviations; 3. Tests based on the maximum likelihood, such as the likelihood ratio test (see appendix A); MODELS FOR THE CLAIM NUMBER DISTRIBUTION 29 4.
The negative binomial model allows a good representation of drivers' behavior. The good quality of the fits suggests that the Poisson hypothesis for individual drivers, and the Gamma hypothesis for the portfolio distribution of claim frequencies, are valid assumptions. Note, however, that there are many different justifications for the use of the negative binomial model, other than the mixed Poisson-Gamma hypothesis (see for instance Panjer and Willmot, 1988a). What is more important, the fact that claims behavior in an insurance portfolio exhibits positive contagion is a statistical proof that the use of a BMS is amply justified.