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Robust Risk Estimation

For risk prediction, the observed past has to be representative for the future, which for extreme events often is at least debatable.

In quantifying risk, usually the tail behavior of the underlying distribution is crucial. Classical procedures for this purpose are drastically prone to outliers: For estimation of the 99.9% quantile from 5000 observations, 5 irreproducible, extra-ordinarily large observations suffice to render the empirical quantile completely meaningless, for instance.  Maximum Likelihood Estimators are no better and still attribute unbounded influence to some exposed observations.   Robust statistics in contrast offers procedures bounding the influence of single observations.

Project "Robust Risk Estimation" addresses theoretical foundation, development and application of robust procedures for risk management for complex systems in the presence of extreme events. It involves  applications in Financial Mathematics (Operational Risk), Medicine (length of stay and cost) and Hydrology (river discharge data). These applications are bridged by the common use of robustness and extreme value statistics.

Our team of mathematicians working in these different application areas jointly tackles identification, quantification, prediction and control of risks occurring in these applications. In suitable parametric models, the goal is to adapt the robustness approach base
d on shrinking neighborhoods to determine stable, and optimally-robust estimators on distributional neighborhoods about the ideal model. In addition, we are going to develop corresponding diagnostic tools to quantify and visualize the influence and outlyingness of data.

Multivariate and Dynamic Extreme Events with Possibly Misspecified Models

Starting from March 1st 2015, the  Volkswagen Foundation is funding the  extension of the project "Robust Risk Estimation". The goals of this second project phase is to capture the dynamics of extreme events,  to take into account the possibility of mis-specified models and the thorough application of the methods developed within the first project phase to real data.
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Funded by VW