  This paper deals with optimally-robust parameter estimation in generalized
Pareto distributions (GPDs). These arise naturally in many situations where one
is interested in the behavior of extreme events as motivated by the
Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have
in mind is calculation of the regulatory capital required by Basel II for a
bank to cover operational risk. In this context the tail behavior of the
underlying distribution is crucial. This is where extreme value theory enters,
suggesting to estimate these high quantiles parameterically using, e.g. GPDs.
Robust statistics in this context offers procedures bounding the influence of
single observations, so provides reliable inference in the presence of moderate
deviations from the distributional model assumptions, respectively from the
mechanisms underlying the PBHT.
