# Extremal Dependence and Probability of Failure: An Application to Fire Insurance Data – University of Copenhagen

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# Extremal Dependence and Probability of Failure: An Application to Fire Insurance Data

Specialeforsvar ved Anna Søgaard Ambrosi

Titel: Extremal Dependence and Probability of Failure:
An Application to Fire Insurance Data

Abstract: The following text is an investigation of the extremal dependence of real-life fire insurance claims from a large Danish non-life insurer. Throughout the text, the theories and methods are applied to this data. Initially, univariate extreme value theory is introduced in order to extend to the multivariate case with a focus on the bivariate case. We use the regular variation property as its backbone and introduce the spectral measure in order to distinguish between asymptotically dependent and asymptotically independent data. Furthermore, a different method for investigating the extremal dependence is analysed. This method, Across Dependence Classes'' (ADC), is derived by Wadsworth et al. It distinguishes between asymptotically dependent and asymptotically independent data through a single parameter, lambda. Furthermore, for each method failure set probabilities were estimated. We look at two datasets; the total dataset which consists of what has been set aside for the claims and the paid dataset consisting of what in fact has been paid out by the insurance company for the claims. Through both methods, the total dataset appeared to be asymptotically dependent, but unexpectedly the paid dataset appeared to be asymptotically independent. The ADC method had some weaknesses; in particular some of the found estimates were out of bounds compared to their respective likelihood regions. Furthermore, there are a lot of restrictions when using this method. In particular the limitation in the choice of norms and censoring approach

Vejledere: Thomas Mikosch, Anja Janssen
Censor:      Mette M Havning