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# On a class of law invariant convex risk measures

Type of Publication: | Journal article |

Publication status: | Published |

Author: | Angelsberg, Gilles; Delbaen, Freddy; Kaelin, Ivo; Kupper, Michael; Näf, Joachim |

Year of publication: | 2011 |

Published in: | Finance and Stochastics ; 15 (2011). - pp. 343-363. - Springer. - ISSN 0949-2984. - eISSN 1432-1122 |

DOI (citable link): | https://dx.doi.org/10.1007/s00780-010-0145-5 |

Summary: |
We consider the class of law invariant convex risk measures with robust representation ρ
_{h,p}(X)=sup_{f}∫^{1}_{0}[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. |

Subject (DDC): | 510 Mathematics |

Refereed: | Yes |

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ANGELSBERG, Gilles, Freddy DELBAEN, Ivo KAELIN, Michael KUPPER, Joachim NÄF, 2011. On a class of law invariant convex risk measures. In: Finance and Stochastics. Springer. 15, pp. 343-363. ISSN 0949-2984. eISSN 1432-1122. Available under: doi: 10.1007/s00780-010-0145-5

@article{Angelsberg2011class-55458, title={On a class of law invariant convex risk measures}, year={2011}, doi={10.1007/s00780-010-0145-5}, volume={15}, issn={0949-2984}, journal={Finance and Stochastics}, pages={343--363}, author={Angelsberg, Gilles and Delbaen, Freddy and Kaelin, Ivo and Kupper, Michael and Näf, Joachim} }