IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v15y2005i4p613-634.html
   My bibliography  Save this article

A Representation Result For Concave Schur Concave Functions

Author

Listed:
  • Rose‐Anne Dana

Abstract

A representation result is provided for concave Schur concave functions on L∞(Ω). In particular, it is proven that any monotone concave Schur concave weakly upper semicontinuous function is the infinimum of a family of nonnegative affine combinations of Choquet integrals with respect to a convex continuous distortion of the underlying probability. The method of proof is based on the concave Fenchel transform and on Hardy and Littlewood's inequality. Under the assumption that the probability space is nonatomic, concave, weakly upper semicontinuous, law‐invariant functions are shown to coincide with weakly upper semicontinuous concave Schur concave functions. A representation result is, thus, obtained for weakly upper semicontinuous concave law‐invariant functions.

Suggested Citation

  • Rose‐Anne Dana, 2005. "A Representation Result For Concave Schur Concave Functions," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 613-634, October.
  • Handle: RePEc:bla:mathfi:v:15:y:2005:i:4:p:613-634
    DOI: 10.1111/j.1467-9965.2005.00253.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9965.2005.00253.x
    Download Restriction: no

    References listed on IDEAS

    as
    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Zilcha, Itzhak & Chew, Soo Hong, 1990. "Invariance of the efficient sets when the expected utility hypothesis is relaxed," Journal of Economic Behavior & Organization, Elsevier, vol. 13(1), pages 125-131, January.
    3. repec:dau:papers:123456789/5446 is not listed on IDEAS
    4. Dana, R. A., 2004. "Market behavior when preferences are generated by second-order stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 619-639, September.
    5. Chew, S H & Epstein, Larry G & Segal, U, 1991. "Mixture Symmetry and Quadratic Utility," Econometrica, Econometric Society, vol. 59(1), pages 139-163, January.
    6. Chongmin Kim, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 341-356.
    7. repec:dau:papers:123456789/6105 is not listed on IDEAS
    8. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    9. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
    10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    11. Peleg, Bezalel & Yaari, M E, 1975. "A Price Characterization of Efficient Random Variables," Econometrica, Econometric Society, vol. 43(2), pages 283-292, March.
    12. Guillaume Carlier & Rose-Anne Dana, 2003. "Pareto efficient insurance contracts when the insurer's cost function is discontinuous," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 871-893, June.
    13. Johannes Leitner, 2005. "A Short Note On Second‐Order Stochastic Dominance Preserving Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 649-651, October.
    14. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    15. repec:dau:papers:123456789/6697 is not listed on IDEAS
    16. repec:dau:papers:123456789/5394 is not listed on IDEAS
    17. Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-1546, November.
    18. repec:dau:papers:123456789/5389 is not listed on IDEAS
    19. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    20. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:15:y:2005:i:4:p:613-634. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.