On law invariant coherent risk measures

  • Shigeo Kusuoka
Part of the Advances in Mathematical Economics book series (MATHECON, volume 3)


The idea of coherent risk measures has been introduced by Artzner, Delbaen, Eber and Heath [1]. We think of a special class of coherent risk measures and give a characterization of it. Let (Ω, ℱ, P) be a probability space. We denote L (Ω, ℱ, P) by L . Following [1], we give the following definition.

Key words

Risk measures value at risk 

JEL Classification


Mathematics Subject Classification (2000)



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  1. 1.
    Artzner, Ph., F. Delbaen, J.-M. Eber, and D. Heath: Coherent measures of risk. Math. Finance 9, 203–228 (1999)CrossRefGoogle Scholar
  2. 2.
    Delbaen, F.: Coherent Risk Measures on General Probability Spaces. Preprint 1999Google Scholar
  3. 3.
    Williams, D.: Probability with Martingales. Cambridge University Press, Cambridge 1991CrossRefGoogle Scholar

Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Shigeo Kusuoka
    • 1
  1. 1.Graduate School of Mathematical SciencesThe University of TokyoMeguro-ku, TokyoJapan

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