One-dimensional spline smoothing in insurance

Abstract

There are lots of special techniques and distribution models used to solve different problems in the insurance industry today. Learning the theory behind all of them is time consuming and leaves little time to analyze results. There are also few techniques and models which work well in situations with little data, and just using the empirical distribution function can lead to the underestimation of future liabilities. This thesis deals with spline smoothing models and their possible applications in the insurance industry. Spline models are simply put piecewise defined polynomial functions with smooth derivatives. When using spline models no view is put on the data, which can be an advantage in situations with little and/or long tailed data. The main objectives of the thesis are; 1. To highlight that there is a need for a general technique which can make models designed for specific purposes obsolete. 2. To show that spline models used together with link-functions can be such a general technique. 3. Write compact and easy to understand programmes that can easily be implemented into standard software.