On a class of law invariant convex risk measures View Full Text


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Article Info

DATE

2010-12-23

AUTHORS

Gilles Angelsberg, Freddy Delbaen, Ivo Kaelin, Michael Kupper, Joachim Näf

ABSTRACT

We consider the class of law invariant convex risk measures with robust representation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho_{h,p}(X)=\sup_{f}\int_{0}^{1} [AV@R_{s}(X)f(s)-f^{p}(s)h(s)]\,ds$\end{document}, 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 ρh,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. More... »

PAGES

343-363

References to SciGraph publications

  • 2002-10. Convex measures of risk and trading constraints in FINANCE AND STOCHASTICS
  • 2008-07-29. Dual characterization of properties of risk measures on Orlicz hearts in MATHEMATICS AND FINANCIAL ECONOMICS
  • 2001. On law invariant coherent risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2006. Law invariant risk measures have the Fatou property in ADVANCES IN MATHEMATICAL ECONOMICS
  • 2005. Law invariant convex risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 1979. Fonction maximale et variation quadratique des martingales en presence d'un poids in SÉMINAIRE DE PROBABILITÉS XIII
  • 1979. Inegalites de normes avec poids in SÉMINAIRE DE PROBABILITÉS XIII
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    http://scigraph.springernature.com/pub.10.1007/s00780-010-0145-5

    DOI

    http://dx.doi.org/10.1007/s00780-010-0145-5

    DIMENSIONS

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