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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

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