Bonus-Malus Systems in Automobile Insurance by Jean Lemaire

By Jean Lemaire

Most insurers around the globe have brought a few type of merit-rating in motor vehicle 3rd social gathering legal responsibility coverage. Such structures, penalizing at-fault injuries via top rate surcharges and profitable claim-free years by way of mark downs, are known as bonus-malus structures (BMS) in Europe and Asia. With the present deregulation traits that crisis such a lot coverage markets world wide, many businesses might want to strengthen their very own BMS. the most target of the booklet is to supply them types to layout BMS that meet their pursuits.
half I of the booklet includes an total presentation of the professionals and cons of merit-rating, a case examine and a assessment of the various chance distributions that may be used to version the variety of claims in an vehicle portfolio. partly II, 30 structures from 22 various international locations, are evaluated and ranked in response to their `toughness' in the direction of policyholders. 4 instruments are created to judge that durability and supply a tentative type of all structures. Then, issue research is used to combination and summarize the information, and supply a last rating of all structures. half III is an updated overview of the entire chance types which have been proposed for the layout of an optimum BMS. the appliance of those versions may let the reader to plot the procedure that's supreme to the habit of the policyholders of his personal assurance corporation. ultimately, half IV analyses a substitute for BMS; the advent of a coverage with a deductible.

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L k=O Pk()")Tk is the transition matrix of this Markov chain. As we shall always assume that the claim frequency is stationary in time (no improvement in the insured's driving ability), the chain is homogeneous. The preceding definition assumes that the BMS forms a Markov chain process. A (first-order) Markov chain is a stochastic process in which 8 MODELS FOR CLAIM NUMBER DISTRIBUTIONS the future development depends only on the present state but not on the history of the process or the manner in which the present state was reached.

The insurer is likely to try to eliminate these bad risks from its portfolio. Alternative Tests. The X2 test is the best known among all goodness-of-fit tests, due to its flexibility. It is the most practical, easy-to-use, flexible test and can be applied in most situations. It is, however, not the most powerful test, due to the discarding of information resulting from the grouping of classes and the arbitrariness in the selection of classes in the continuous case. Many other tests have been presented in the statistics literature (see Albrecht, 1982b, and D' Agostino and Stephens, 1986, for reviews of goodness-of-fit tests).

The only subject of the meeting was "No-Claim Discount in Insurance, with Particular Reference to Motor Business". Volume I of the ASTIN Bulletin contains some of the contributions to this colloquium. The negative binomial distribution was discussed by Bichsel (1960), Thyrion (1960), Pesonen (1962), Derron (1962, 1963), and Delaporte (1965). A two-point mixing distribution for the Poisson was already mentioned in Derron (1963). Other mixed Poisson models have been considered in the actuarial literature: * Willmot (1986, 1993) developed a simple recursive formula that holds for a wide variety of continuous mixing distributions.

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