Delbaen, Freddy; Bellini, Fabio; Bignozzi, Valeria; Ziegel, Johanna F. (2016). Risk measures with the CxLS property. Finance and stochastics, 20(2), pp. 433-453. Springer 10.1007/s00780-015-0279-6
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In the present contribution, we characterise law determined convex risk
measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Ziegel, Johanna F. |
Subjects: |
300 Social sciences, sociology & anthropology > 360 Social problems & social services 500 Science > 510 Mathematics |
ISSN: |
0949-2984 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Lutz Dümbgen |
Date Deposited: |
02 Dec 2015 10:38 |
Last Modified: |
05 Dec 2022 14:50 |
Publisher DOI: |
10.1007/s00780-015-0279-6 |
ArXiv ID: |
1411.0426v1 |
Uncontrolled Keywords: |
Decision theory; Elicitability; Convex level sets; Mixture continuity; Robustness; 62C05; 91B30; 62G35; D81; C44 |
BORIS DOI: |
10.7892/boris.73266 |
URI: |
https://boris.unibe.ch/id/eprint/73266 |
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