An extreme value analysis of motor insurance data

Specialeforsvar ved Karoline Ellesgaard Norby

Titel: An extreme value analysis of motor insurance data

Abstract: This thesis studies large claims from UK motor insurance data, using extreme value theory. The data consists of the two variables, liability and hull claims. In the first part of the thesis, the univariate theory is introduced and used to examine The tail index and the tail distribution in three different ways. The three methods do not agree on the estimation of the tail index for the liability claims. However the methods do agree on the estimate for the hull claims. The two parameter method peaks over threshold, turns out to be the best method to estimate the tail index and the tail distribution for this specific data. The univariate theory and analysis allows one to extend to the bivariate theory. In the bivariate case, the dependence structure between the variables is analysed by the angular measure. Further, the bivariate theory of failure sets is used to study the probability that a future claim lies in a certain catastrophic set.

The dependence structure is studied using two different modifications of the data and further from two different angles. From the first angle, the dependence structure for the liability andhull claims is studied and in the second, the focus is on the dependence between final paid and first reserved claim amounts. In the last part of the thesis, the theory of failure sets is used to estimate failure probabilities. Essential tools for this theory are the angular measure and the homogeneity property, which permits estimation of probabilities, in areas where no claims have been observed.

Vejleder: Thomas Mikosch
Censor:   Mette Havning