Risk measures with the CxLS property
Risk Management
2014-11-04 v1
Abstract
In the present contribution we characterize law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (2006), we show that these risk measures can be identified with a class of generalized shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (2014) and Bellini and Bignozzi (2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterization of robustness for convex risk measures in terms of a weak notion of mixture continuity.
Keywords
Cite
@article{arxiv.1411.0426,
title = {Risk measures with the CxLS property},
author = {Freddy Delbaen and Fabio Bellini and Valeria Bignozzi and Johanna F. Ziegel},
journal= {arXiv preprint arXiv:1411.0426},
year = {2014}
}