Use of Spline Functions for Premium Rating by Geographic Area

The paper gives details of a case study on 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.