Bivariate extreme value analysis of insurance data

Specialeforsvar ved Morten Korthé Carlsen

Titel: Bivariate extreme value analysis of insurance data

Abstract : In Solvency II the solvency capital requirement is based on the non-life underwriting risk, of which large claims constitute a significant amount.
Such large claims have different characteristics to standard insurance claims as they deviate significantly from the median and occur infrequently.
Hence, an alternative approach to the standard approach of fitting a distribution to the dataset is to use extreme value theory.Two essential quantities to estimate are the tail of the underlying distribution and the quantiles used to describe the extremal behaviour of the data.
The data set examined here is the lossalaefull set which consists of liability claims and the corresponding ALAE payments. Accordingly, a univariate analysis is performed with a focus on the Hill method and POT method to estimate the tail and quantiles.
An extension to the multivariate case is examined whereby the dependence structure between the two types of payments is explored and the spectral measure is used.
Finally, the concept of failure sets is introduced. Different types of failure sets are considered, the probability of the stochastic variables exceeding certain thresholds is estimated by extrapolating beyond observed data.

Vejleder: Thomas V Mikosch
Censor:   Yuri Goegebeur, SDU