Risk measures with the CxLS property

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:

25 Apr 2017 23:44

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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