Generalized Linear Models and Their Applications to Actuarial Modeling

This paper will discuss the basic principles underlying the theory of generalized linear models and the advantages of using generalized linear models over more traditional methods of actuarial modeling. Generalized linear models offer the flexibility needed to model real world data that does not conform to the strict assumptions underlying these traditional methods. The second part ofthis paper will illustrate how generalized linear models can be directly applied to current areas of actuarial practice, and the advantages that are to be gained. The Standard Linear Model The world is filled with many phenomena that upon close observation are clearly related. For example, economists know that interest rates and inflation tend to move in the same direction. When profits decline, unemployment rises. When weather conditions worsen, drivers have more accidents. Actuaries are interested in modeling relationships such as these. While the exact relationship between two such phenomena may not be known, past observations can be used to estimate their relationship and thus form a model which will allow us to more accurately predict future observations. One possible tool that might be used is the standard linear model. The standard linear model relates two variables such that