Bridging Minimum Bias and Maximum Likelihood Methods Through Weighted Equation

In classification ratemaking, the multiplicative and additive models derived by actuaries are based on two common methods; minimum bias and maximum likelihood. These models are already considered as established and standard, particularly in automobile and general liability insurance. This paper aims to identify the relationship between both methods by rewriting the equations of both minimum bias and maximum likelihood as a weighted equation. The weighted equation is in the form of a weighted difference between observed and fitted rates. The advantage of having the weighted equation is that the solution can be solved using regression model. Compared to the classical method introduced by Bailey and Simon (1960), the regression model provides an improved and simplified programming algorithm. In addition, the parameter estimates could also be rewritten as a weighted solution; for multiplicative model the solution can be written in the form of a weighted proportion whereas for additive model, the form is of a weighted difference. In this paper, the weighted equation will be applied on three types of classification ratemaking data; ship damage incidents data of McCullagh and Nelder (1989), data from Bailey and Simon (1960) on Canadian private automobile liability insurance and UK private car motor insurance data from Coutts (1984).