The effect of smoothing splines on pricing of non-life insurance products

The Generalized Linear Models (GLM) is one of the most commonly used methods of pricing non-life insurance products. The method gives a great advantage for selecting loss distribution from exponential family. Typically loss distributions are right-skewed and long-tailed which means the appropriate distributions are Poisson distribution for claim frequency and Gamma distribution for claim severity. Non-life insurance data involves several continuous variables. GLM categorizes the continuous variables into intervals and treats them as identical. However, categorizing the continuous variables method has no common rules and as a result of that it causes some information loss at the breaking points. Instead of categorizing the continuous variables there is an alternative method which is known as Generalized Additive Models. (GAM) provides an alternative modelling without transforming continuous variables into categorical variables. GAM method has same properties with GLM except a semiparametric model with a smoothing spline add-on. In other definition GAM is semiparametric GLM. The biggest advantage of GAM is that the model is flexible with semi-parametric formation. By flexibility we mean that continuous variables are to be included in the model as smoothing splines. In this case, the information on each point of the continuous variable is included in the model. The optimal value for the smoothing parameter is automatically selected by the cross-validation approach for the spline function. The aim of this thesis is to study the use of cubic smoothing splines represented in the B-spline form for the effect of continuous variables in the GAM method. Generalized Additive Models and Generalized Linear Models is compared through the insurance loss dataset applications and the research question is answered.