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Two Studies in Automobile Insurance Ratemaking

Published online by Cambridge University Press:  29 August 2014

Robert A. Bailey  and
LeRoy J. Simon
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Section A of this paper uses the Canadian experience for private passenger automobiles to show (1) that merit rating is almost as effective as the class plan in separating the better risks from the poorer risks, (2) that both merit rating and class rating leave unanalyzed a considerable amount of variation among risks and (3) that certain available evidence supports the conclusion that annual mileage, which has long been felt to be an important measure of hazard, is a very significant cause of this unanalyzed variation among risks.

Section B presents a method for obtaining relativities among groups on which a multiple classification system has been imposed. The customary method of calculating class relativities uses the total experience for each class with all subdivisions within the classes added together. With the customary method it is difficult to make a completely accurate adjustment for different distributions by territory or merit rating, because any change in the class relativities disturbs the other sets of relativities and conversely. It is shown that even if such an adjustment were made, the customary method of calculating relativities one set at a time does not reflect the relative credibility of each subgroup and does not produce the best fit to the actual data. Moreover it produces differences between the actual data and the fitted values which are far too large to be caused by chance. In addition, for private passenger automobile insurance in Canada, it is shown that two sets of relativities which are multiplied together cannot produce the best fit to the actual data, and some of the consequences of trying to do so are explained. Some methods are advanced whereby all sets of relativities for classes, merit ratings, territories, and so forth, can be calculated simultaneously, which will overcome all the deficiencies in the customary method. These improved methods use the technique of minimizing a measure (technically known as the chi-square test) of the differences between the actual data and the fitted values. Some applications to other lines of insurance are mentioned.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 1 , Issue 4 , December 1960 , pp. 192 - 217
Copyright
Copyright © International Actuarial Association 1960

References

page 193 note 1) See also “Some Considerations on Automobile Rating Systems Utilizing Individual Driving Records” by Dropkin, Lester, Proceedings of the Casualty Actuarial Society (hereafter PCAS) XLVI, p. 165Google Scholar.

page 194 note 1 The Canadian experience includes that of virtually every insurance company operating in Canada and is collated by the Statistical Agency (Canadian Underwriters' Association — Statistical Department) acting under instructions from the Superintendent of Insurance.

page 195 note 1 See Muir, J. M., “Principles and Practices in Connection With Classification Rating Systems for Liability Insurance As Applied to Private Passenger Automobiles”, PCAS XLIV, pp. 32 and 33Google Scholar.

page 195 note 2) Bailey, Robert A. and Simon, LeRoy J., “An Actuarial Note on the Credibility of Experience of a Single Private Passenger Car”, PCAS; XLVI; Table 1, p. 162Google Scholar. This table is reproduced here for convenient reference as Table 3.

page 196 note 1) Op. Cit.

page 196 note 2) Bailey, Robert A. and Simon, LeRoy J., Op. Cit., Table 4, p. 163. This table is reproduced here for convenient reference as Table 4.

page 197 note 1) Bailey, Robert A. Discussion, “Some Considerations on Automobile Hating Systems Utilizing Individual Driving Records”, PCAS, XLVII.

page 197 note 2) OP. cit. This table is reproduced here (or convenient reference as Table 4.

page 198 note 1) See DeSilva, Harry R.Why We Have Automobile Accidents. John Wiley & Sons, New York, 1942, p. 12Google Scholar.

page 198 note 2) Ibid., p. 13.

page 203 note *) For example, see “Current Rate Making Procedures for Automobile Liability Insurance”, Stern, Phillip K., PCAS XLIII, p. 127 ff.Google Scholar

page 211 note *) See Stern, Op. Cit., p. 154 and Livingston, G. R., & Carlson, T. O., discussion of “Principles and Practices in Connection with Classification Rating Systems for Liability Insurance as Applied to Private Passenger Automobiles”. PCAS XLV, p. 230Google Scholar.