Skip to main content

The representations of two types of functionals on L (Ω, Ƒ) and L (Ω, Ƒ, ℙ)

Abstract

This article gives the representations of two types of real functionals on L (Ω, Ƒ) or L (Ω, Ƒ, ℙ) in terms of Choquet integrals. These functionals are comonotonically subadditive and comonotonically convex, respectively.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Artzner P, Delbaen F, Eber J M, Heath D. Thinking coherently. RISK, 1997, 10: 68–71

    Google Scholar 

  2. 2

    Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk. Math Finance, 1999, 9(3): 203–228

    MATH  MathSciNet  Article  Google Scholar 

  3. 3

    Delbaen F. Coherent risk measures. Lecture notes, Pisa. 2001

  4. 4

    Delbaen F. Coherent measures of risk on general probability spaces. In: Advancees in Finance and Stochastics. Berlin: Springer-Verlag, 2002, 1–37

    Google Scholar 

  5. 5

    Föllmer H, Schied A. Convex measures of risk and trading constraints. Finance and Stochastics, 2002, 6(4): 429–447

    MATH  MathSciNet  Article  Google Scholar 

  6. 6

    Frittelli M, Rosazza Gianin E. Putting order in risk measures. J Banking Finance, 2002, 26(7): 1473–1486

    Article  Google Scholar 

  7. 7

    Huber P J, ed. Robust Statistics. New York: Wiley, 1981

    MATH  Google Scholar 

  8. 8

    Denneberg D. Non-additive Measure and Integral. Boston: Kluwer Academic Publishers, 1994

    MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Song Yongsheng.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Song, Y., Yan, J. The representations of two types of functionals on L (Ω, Ƒ) and L (Ω, Ƒ, ℙ). SCI CHINA SER A 49, 1376–1382 (2006). https://doi.org/10.1007/s11425-006-2010-8

Download citation

Keywords

  • Choquet integral
  • comonotonically subadditive
  • comonotonically convex