Advanced Search
MyIDEAS: Login to save this article or follow this journal

Comonotonicity, efficient risk-sharing and equilibria in markets with short-selling for concave law-invariant utilities

Contents:

Author Info

  • Dana, R.-A.
Registered author(s):

    Abstract

    In finite markets with short-selling, conditions on agents’ utilities insuring the existence of efficient allocations and equilibria are by now well understood. In infinite markets, a standard assumption is to assume that the individually rational utility set is compact. Its drawback is that one does not know whether this assumption holds except for very few examples as strictly risk averse expected utility maximizers with same priors. The contribution of the paper is to show that existence holds for the class of strictly concave second order stochastic dominance preserving utilities. In our setting, it coincides with the class of strictly concave law-invariant utilities. A key tool of the analysis is the domination result of Lansberger and Meilijson that states that attention may be restricted to comonotone allocations of aggregate risk. Efficient allocations are characterized as the solutions of utility weighted problems with weights expressed in terms of the asymptotic slopes of the restrictions of agents’ utilities to constants. The class of utilities which is used is shown to be stable under aggregation.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000322
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 3 ()
    Pages: 328-335

    as in new window
    Handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:328-335

    Contact details of provider:
    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Law invariant utilities; Comonotonicity; Pareto efficiency; Equilibria with short-selling; Aggregation; Representative agent;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922 Elsevier.
    2. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print, HAL halshs-00176522, HAL.
    3. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(10), pages 1181-1188, August.
    4. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
    5. Touzi, Nizar & Schachermayer, Walter & Jouini, Elyès, 2006. "Law Invariant Risk Measures Have the Fatou Property," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/342, Paris Dauphine University.
    6. Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, Springer, vol. 12(3), pages 423-439, July.
    7. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 18(2), pages 269-292.
    8. Dana, Rose-Anne & Carlier, Guillaume, 2008. "Two-Persons Efficient Risk-Sharing and Equilibria for Concave Law-Invariant Utilities," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/2348, Paris Dauphine University.
    9. Florenzano, Monigue & Le Van, Cuong, 1986. "A note on the Gale-Nikaido-Debreu lemma and the existence of general equilibrium," Economics Letters, Elsevier, Elsevier, vol. 22(2-3), pages 107-110.
    10. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 169-193, July.
    11. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, Elsevier, vol. 52(2), pages 153-162, August.
    12. Dana, Rose-Anne & Le Van, Cuong, 1996. "Arbitrage, duality and asset equilibria," CEPREMAP Working Papers (Couverture Orange) 9613, CEPREMAP.
    13. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1103-23, November.
    14. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 20(1), pages 137-152.
    15. Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 598, University of Warwick, Department of Economics.
    16. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
    17. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer, Springer, vol. 36(2), pages 189-223, August.
    18. Jouini, Elyès & Schachermayer, Walter & Touzi, Nizar, 2008. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/361, Paris Dauphine University.
    19. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:328-335. 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: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.