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Estimation of tail quantities, such as expected shortfall or Value at Risk,is a difficult problem. We show how the theory of nonlinear expectations, inparticular the Data-robust expectation introduced in [5], can assist in thequantification of statistical uncertainty for these problems. However, when weare in a heavy-tailed context (in particular when our data are described by aPareto distribution, as is common in much of extreme value theory), the theoryof [5] is insufficient, and requires an additional regularization step which weintroduce. By asking whether this regularization is possible, we obtain aqualitative requirement for reliable estimation of tail quantities and riskmeasures, in a Pareto setting.

Data and uncertainty in extreme risks - a nonlinear expectations approach