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.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Artzner P, Delbaen F, Eber J M, Heath D. Thinking coherently. RISK, 1997, 10: 68–71
Artzner P, Delbaen F, Eber J M, Heath D. Coherent measures of risk. Math Finance, 1999, 9(3): 203–228
Delbaen F. Coherent risk measures. Lecture notes, Pisa. 2001
Delbaen F. Coherent measures of risk on general probability spaces. In: Advancees in Finance and Stochastics. Berlin: Springer-Verlag, 2002, 1–37
Föllmer H, Schied A. Convex measures of risk and trading constraints. Finance and Stochastics, 2002, 6(4): 429–447
Frittelli M, Rosazza Gianin E. Putting order in risk measures. J Banking Finance, 2002, 26(7): 1473–1486
Huber P J, ed. Robust Statistics. New York: Wiley, 1981
Denneberg D. Non-additive Measure and Integral. Boston: Kluwer Academic Publishers, 1994
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11425-006-2010-8