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Title: Flexible extreme value modelling in insurance and finance Authors:  Gaonyalelwe Maribe - University of Pretoria (South Africa) [presenting]
Abstract: Extreme value theory (EVT) is used to model rare events (extreme observations). One particular approach in EVT is the Peaks over threshold (POT) method, which employs the asymptotically motivated generalized Pareto distribution (or simple Pareto) to model exceedances (or relative excesses) above a sufficiently high threshold. The choice of this threshold however remains an open question. In recent years several attempts have been made to extend tail modelling towards the modal part of the data. Dynamic mixtures of two components with a weight function smoothly connecting the bulk and the tail of the distribution has been proposed. Most recently a review of this topic has been made, along with a statistical model which is in compliance with extreme value theory and allows for a smooth transition between the modal and tail part. We discuss special cases of these approaches and revisit and extend the second order refined POT approach to all max-domains of attraction using flexible semiparametric modelling of the second order component. Practical cases in insurance and finance are given were such models can be of importance.