Analysis of Multivariate Extremes in Fire Insurance data

Specialeforsvar ved Gabrielle Opris Mogensen 

Titel: Analysis of Multivariate Extremes in Fire Insurance data

Abstract: The theory of multivariate extremes has garnered increasing attention over the years since many applications of extreme value theory are intrinsically multivariate. Especially for environmental subjects, such as the study of wave heights, water levels, or rain fall in connection to floods, it can be seen to be of great value. In this thesis, we consider some aspects of multivariate extreme value theory pertaining to bivariate fire insurance data, consisting of industrial fire insurance claims divided into damage to buildings and damage to the movable property within. Fire insurance claims have generally been observed to be heavy-tailed, and it is intuitively clear that there is a strong dependence between the two types of damages. Following the work of de Haan & de Ronde, de Haan & Ferreira, and Resnick, we present a theory of multivariate extremes in terms of the fluctuations of affine transformations of component-wise maxima. We also consider estimation of probabilities of events that have not yet occurred, and the problem of estimation when there is no data available in the region of interest. Furthermore, we discuss a multivariate extension of the univariate peaks over threshold method as a possible way of modelling excesses of high thresholds in a multivariate context. We also consider the close connection between multivariate extreme value distributions and the representation of multivariate Pareto distributions suggested by Tajvidi & Rootzén. Lastly, we consider some of the issues that arise when expanding from a bivariate framework to higher dimensions on simulated datasets

Vejleder:  Thomas Mikosch
Censor:    Søren Asmussen, Aarhus Universitet