Risk measures with the CxLS property |
| |
| Authors: | Freddy Delbaen Fabio Bellini Valeria Bignozzi Johanna F Ziegel |
| |
| Institution: | 1.Department of Mathematics,ETH Zurich,Zurich,Switzerland;2.Institute for Mathematics,University of Zurich,Zurich,Switzerland;3.Department of Statistics and Quantitative Methods,University of Milano Bicocca,Milan,Italy;4.Department of Methods and Models for Economics, Territory and Finance,Sapienza University of Rome,Rome,Italy;5.Institute of Mathematical Statistics and Actuarial Science,University of Bern,Bern,Switzerland |
| |
| Abstract: | 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. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
