Minimum Bias With Generalized Linear Models

The paper "Insurance Rates with Minimum Bias" by Robert A. Bailey [3] presents a methodology which is used by a large number of Canadian casualty actuaries to determine class and driving record differentials. In his paper, Bailey outlines four methods (two directly and two by reference to a previous paper by Bailey and Simon). No presentation has ever been made of an analysis of the applicability of these methods on Canadian data. Also, no attempt has been made within the Casualty Actuarial Society literature to augment Bailey's discussion using other statistical approaches now familiar to members of the Society. This paper analyzes the four Bailey methodologies using Canadian data and then introduces five models using a modern statistical approach. (It should be noted that one of these statistical models turns out to be a reproduction of one of Bailey's models.) The paper then gives a brief study of generalized linear models followed by an explanation of one possible way of mathematically modeling the specified Canadian data to the given models on the computer using a statistical software package called GLIM (Generalized Linear Interactive Modeling). Keywords: Class Rating, Territorial Rating