An actuarial approach to motor insurance rating
This thesis describes an actuarial structure for the practical analysis of motor insurance premium rating. An underlying theme emphasises that judgements are being made taking into account many factors e.g. economical, statistical and technical, therefore it is necessary to bring into the decision process a group of interested persons. In addition even though data are used to explain the proposed methods, it is the framework which is important and not the omission of some of the data e.g. important rating factors. The basis for premium projecting is discussed together with a critical discussion of various measures of surplus. A new measure is developed referred to as 'proposed to existing' which measures the effect of premium adjustments after taking into account the portfolio distribution. Another theme is to encourage a detailed within-portfolio analysis. An example, using data supplied by an Insurance Company helps to highlight the structure. The analysis commences by sub-dividing the data into important underwriting rating factors. The claim experience is further divided by claim proportions and the three main types of claims cost: accidental damage, third party property damage and third party bodily injury. By sub-dividing the data into multiway cells both exposure and claim numbers become very small, hence statistical modelling is used to smooth the data and to reduce variation. A critical review of past models in respect of claim proportions and accidental damage costs is made. In addition a pragmatic approach to third party bodily injury is carried out. To obtain an office premium the modelled claim experience is combined with economic factors such as inflation and expenses. Details of fitting the additive model by Orthogonal Weighted Least Squares is described. This converts the office premium into a 'points table'. An advantage of this 'points table' is that it can be used to compare various different sets of assumptions. A brief reference to the competitive market position is then made. An analysis of surplus is developed together with a worked example, which highlights the importance of claim proportions and the level of claims cost. Finally, the last chapter gives a summary of further research work which has been indicated as this thesis has developed.