Risk measures with the CxLS property

2014/11/03 by Freddy Delbaen, Fabio Bellini, Delbaen, Freddy +5 · 2 citations
Economics, Econometrics and Finance · #FOS: Economics and business #Risk Management (q-fin.RM) #q-fin.RM

paper · pdf · doi:10.48550/arxiv.1411.0426

arxiv created 2014/11/03 · arxiv updated 2014/11/04

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.

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• Gradient-based Stochastic Optimization of Utility-based Shortfall Risk
• Expectiles as basis risk-optimal payment schemes in parametric insurance

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