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Geographic Premium Rating by Whittaker Spatial Smoothing

Published online by Cambridge University Press:  29 August 2014

Greg Taylor
Greg Taylor*
Affiliation:
Taylor Fry Consulting Actuaries, Sydney Australia andUniversity of Melbourne, Australia
*
Taylor Fry Consulting Actuaries, Level 4, 5 Elizabeth Street, Sydney NSW 2000, Australia
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Abstract

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Whittaker graduation is applied to the spatial smoothing of insurance data. Such data (e.g. claim frequency) form a surface over the 2-dimensional geographic domain to which they relate. Observations on this surface are subject to sampling error. They need to be smoothed spatially if a reliable estimate of the underlying surface is to be obtained.

A measure of smoothness of a surface has been defined. This has been incorporated in 2-dimensional Whittaker graduation to effect the necessary smoothing. The details of this are worked out in Section 4. The procedure is illustrated by numerical example in Section 5. The Bayesian interpretation of this form of spatial smoothing is discussed, and used to assist in the selection of the Whittaker relativity constant.

Keywords

Geographic premium ratingspatial smoothingWhittaker graduation
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 147 - 160
Copyright
Copyright © International Actuarial Association 2001

References

Bailey, T.C. and Gatrell, A.C. (1995) Interactive spatial data analysis. Longman, England.Google Scholar
Boskow, M. and Verrall, R.J. (1994) Premium rating by geographic area using spatial models. ASTIN Bulletin 24, 131–143.CrossRefGoogle Scholar
Brockman, M.J. and Wright, T.S. (1992) Statistical motor rating: making effective use of your data. In Journal of the Institute of Actuaries 119, 457–526.CrossRefGoogle Scholar
Green, P.J. and Silverman, B.W. (1994) Non-parametric regression and generalised linear models: a roughness penalty approach. Chapman and Hall, London, New York.CrossRefGoogle Scholar
Henderson, R. (1924) A new method of graduation. In Transactions of the Actuarial Society of America 25, 29–40.Google Scholar
London, R. (1985) Graduation: the revision of estimates. ACTEX, Winsted and Abington, CT.Google Scholar
Lowrie, W.B. (1992) Multidimensional Whittaker-Henderson graduation with constraints and mixed differences. In Transactions of the Society of Actuaries 45, 215–255.Google Scholar
McKay, S.F. and Wilkin, J.C. (1977) Derivation of a two-dimensional Whittaker-Henderson type B graduation formula. Appendix to Experience of Disabled-Worker Benefits Under OASDI, 1965-74. Actuarial Study No. 74, U.S. Department of Health, Education, and Welfare.Google Scholar
Taylor, G.C. (1989) Use of spline functions for premium rating by geographic area. ASTIN Bulletin 19, 91–122.CrossRefGoogle Scholar
Taylor, G.C. (1992) A Bayesian interpretation of Whittaker-Henderson graduation. In Insurance: mathematics and economics 11, 7–16.Google Scholar
Verrall, R.J. (1993) A state space formulation of Whittaker graduation, with extensions. In Insurance: mathematics and economics 13, 7–14.Google Scholar
Whittaker, E.T. (1923) On a new method of graduation. In Proceedings of the Edinburgh Mathematical Society 41, 63–75.CrossRefGoogle Scholar