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Corpus ID: 220347448

Minkowski gauges and deviation measures

@article{Moresco2020MinkowskiGA,
title={Minkowski gauges and deviation measures},
author={M. Moresco and M. Righi and Eduardo Horta},
journal={arXiv: Risk Management},
year={2020}
}

We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink a position for it to become acceptable. In particular, the Minkowski gauge of a set which is convex, stable under scalar addition, and radially… Expand