Data and uncertainty in extreme risks - a nonlinear expectations approach
Statistics Theory
2018-02-15 v2 Probability
Statistical Finance
Statistics Theory
Abstract
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [5] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting.
Cite
@article{arxiv.1705.08301,
title = {Data and uncertainty in extreme risks - a nonlinear expectations approach},
author = {Samuel N. Cohen},
journal= {arXiv preprint arXiv:1705.08301},
year = {2018}
}