Applications of risk theory and multivariate analysis in insurance practice

Segmentation strategies and differentiated preselection in underwriting call for new portfolio management techniques, the use of which is becoming increasingly widespread amongst insurance companies faced with growing competitive pressure. In recent years, mathematical procedures have been developed for this purpose and the applicability of existing procedures for use in insurance practice has been recognized. The present paper elucidates various methods for determining the aggregate claims distribution, which describes the performance and volatility of a portfolio. There then follows a presentation of multivariate methods, particularly generalized linear models and methods applying variance and discriminant analysis, which facilitate the analysis of more narrowly defined segments and subportfolios. Finally, the paper contains a description of applications used by numerous insurance companies, primarily for motor and property portfolios.