Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-16T23:27:34.729Z Has data issue: false hasContentIssue false
  • English
  • Français

Use of Spline Functions for Premium Rating by Geographic Area

Published online by Cambridge University Press:  29 August 2014

G. C. Taylor
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper gives details of a case study in the premium rating of a Householders Contents insurance portfolio. The rating is performed by the fitting of bivariate spline functions to a version of operating ratio described in Section 3.

The use of bivariate splines requires a small amount of mathematical equipment, which is developed in Section 4. The fitting of splines, using regression is carried out in Sections 5 and 6, where the numerical results are given, including some assessment of goodness-of-fit.

Contour maps of the spline surfaces are also given, and used for the selection of geographic areas used for premium rating purposes. These are compared with the areas, past and present, actually used by the insurer concerned.

Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 1 , April 1989 , pp. 91 - 122
Copyright
Copyright © International Actuarial Association 1989

References

Greville, T. N. E. (1969) (ed). Theory and applications of spline functions. Academic Press, Inc. New York.Google Scholar
Payne, C. D. (1985) (ed). The Generalised Linear Interactive Modelling System. Manual Release 3.77. Numerical Algorithms Group Ltd, Oxford, UK.Google Scholar
Seal, H. L. (1969). Stochastic theory of a risk business. John Wiley & Sons, Inc. New York.Google Scholar
Seal, H. L. (1977). Approximations to risk theory's F(x, t) by means of the gamma distribution. ASTIN-Bulletin, 9, 213–218.CrossRefGoogle Scholar
Seber, G. A. F. (1977). Linear Regression analysis. John Wiley & Sons, Inc. New York.Google Scholar