caa a22 4500 445363355 CHVBK 20180317142922.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00780-010-0145-5 doi (NATIONALLICENCE)springer-10.1007/s00780-010-0145-5 On a class of law invariant convex risk measures [Elektronische Daten] [Gilles Angelsberg, Freddy Delbaen, Ivo Kaelin, Michael Kupper, Joachim Näf] We consider the class of law invariant convex risk measures with robust representation $\rho_{h,p}(X)=\sup_{f}\int_{0}^{1} [AV@R_{s}(X)f(s)-f^{p}(s)h(s)]\,ds$, where 1≤p<∞ and h is a positive and strictly decreasing function. The supremum is taken over the set of all Radon-Nikodým derivatives corresponding to the set of all probability measures on (0,1] which are absolutely continuous with respect to Lebesgue measure. We provide necessary and sufficient conditions for the position X such that ρ h,p(X) is real-valued and the supremum is attained. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and compare them to the average value at risk. Springer-Verlag, 2010 Law invariant convex risk measures nationallicence Robust representation nationallicence Variational methods nationallicence Angelsberg Gilles Commissariat aux Assurances, 2449, Luxembourg, Luxembourg aut Delbaen Freddy Department of Mathematics, ETH Zurich, 8092, Zürich, Switzerland aut Kaelin Ivo Department of Mathematics, ETH Zurich, 8092, Zürich, Switzerland aut Kupper Michael Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Näf Joachim Institute for Theoretical Physics, University of Zurich, 8057, Zürich, Switzerland aut Finance and Stochastics Springer-Verlag 15/2(2011-06-01), 343-363 0949-2984 15:2<343 2011 15 780 https://doi.org/10.1007/s00780-010-0145-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00780-010-0145-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Angelsberg Gilles Commissariat aux Assurances, 2449, Luxembourg, Luxembourg aut NATIONALLICENCE 700 1- Delbaen Freddy Department of Mathematics, ETH Zurich, 8092, Zürich, Switzerland aut NATIONALLICENCE 700 1- Kaelin Ivo Department of Mathematics, ETH Zurich, 8092, Zürich, Switzerland aut NATIONALLICENCE 700 1- Kupper Michael Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 700 1- Näf Joachim Institute for Theoretical Physics, University of Zurich, 8057, Zürich, Switzerland aut NATIONALLICENCE 773 0- Finance and Stochastics Springer-Verlag 15/2(2011-06-01), 343-363 0949-2984 15:2<343 2011 15 780 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer