Coherent Risk Measures and Convex Combinations of the Conditional Value at Risk (C V@R)
DOI:
https://doi.org/10.17713/ajs.v31i1.471Abstract
The conditional-value-at-risk (C V@R) has been widely used as a risk measure. It is well known, that C V@R is coherent in the sense of Artzner, Delbaen, Eber, Heath (1999). The class of coherent risk measures is convex. It was conjectured, that all coherent risk measures can be represented as convex combinations of C V@R’s. In this note we show that this conjecture is wrong.References
P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath. Coherent measures of risk. Mathematical Finance, 9:203–228, 1999.
P.C. Fishburn. Stochastic dominance and moments of distributions. Mathematics of Operations Research, 5:94–100, 1980.
G. Pflug. Some remarks on the Value-at-Risk and the conditional Value-at-Risk. In S. Uryasev, editor, Probabilistic Constrained Optimization – Methodology and Applications, pages 272–281, Kluwer Academic Publishers, 2000.
S. Uryasev and R.T. Rockafellar. Optimization of conditional Value-at-Risk. The Journal of Risk, 2(3):21–41, 2000.
S. Uryasev. Conditional Value-at-Risk: Optimization algorithms and applications. Financial Engineering News 14, February 2000.
Downloads
Published
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
How to Cite
