Multivariate Extreme Value Theory

Specialeforsvar: Frederik Brink

Titel: Multivariate Extreme Value Theory - with an Application in Reserving

Abstract: Many applications of statistics focus on estimating mean values. This thesis will focus on the rare observations far from the mean value. We will cover the theory of univariate and multivariate extreme value theory as tools to analyse extreme and rare observations. Multivariate extreme value theory introduces a dependence model of the extreme observations and this theory will be applied in a reserving context. In practice, the reserving actuary will often exclude extreme values (large claims) from the triangles when applying the chain ladder method. This practice will lead to better predictions of the frequency claims close the mean. However, the question naturally arises how the actuary should deal with large claims? Multidimensional extreme value theory applied in two dimensions yields some theory to discuss the quality of the first case estimate done by the claims department. And then gives the actuary the needed picture of the consequences of leaving out the large claims from the triangles.

Vejleder: Thomas Mikosch
Censor:    Mette Havning