Combined loss reserving and premium rating by GLM

Generalised Linear Models (GLM) are routinely used in two different areas of actuarial work: Loss Reserving and Premium Rating. There is little overlap between the two areas: The loss reserving model attempts to model the development of claims but pays little attention to the effect of risk variables. The premium rating model attempts to model the effect of risk variables on claim patterns ( Frequency and/ or severity) but usually assumes that the claims anaylsed are fully developed. In this dissertation, we aim to bridge the gap between these two areas of actuarial work by developing a Premium Rating model that incorporates risk variables. Specifically, we will consider demographic characteristics such as gender in claim patterns. By doing so, we hope to provide a more comprehensive understanding of the factors that contribute to insurance claims and improve insurers' ability to accurately price their policies, something which can be done in GLM but not in the original Chain Ladder or Bornheutter Ferguson methods. The GLM approach is applied to real-life statistics of professional health insurance that is sold to two risk groups, females and males. The results show that with the inclusion of the risk_group variable in the GLM model framework, females have higher claim cost per insured than males, plus that the number of females is increasing whiles the number of males is falling. The increase in the proportion of females is partly explained by the fact that more females are entering the profession. In a competitive market, the insurance company could risk adverse selection, if at the same time, as more women enter, the lower-risk group (males) starts falling because premiums are becoming too high. EU regulation does not allow insurers to differentiate premiums by sex. Therefore, the insurance company would have to find other ways than premium differentiation, to prevent or reduce adverse selection. It is not my purpose to suggest what the company could do. The purpose of this dissertation is to demonstrate that the use of a GLM in loss reserving may show up facts that would remain concealed if one only used a simple chain ladder method on aggregate statistics. The theoretical base of this work is standard; its challenge lies in applying GLM to realistic datasets and studying the results.