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Equilibrium Prices For Monetary Utility Functions

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  • DAMIR FILIPOVIĆ

    ()
    (Vienna Institute of Finance (Supported by WWTF (Vienna Science and Technology Fund)), University of Vienna and Vienna University of Economics and Business Administration, Heiligenstädter Strasse 46–48, A-1190 Vienna, Austria)

  • MICHAEL KUPPER

    ()
    (Vienna Institute of Finance (Supported by WWTF (Vienna Science and Technology Fund)), University of Vienna and Vienna University of Economics and Business Administration, Heiligenstädter Strasse 46–48, A-1190 Vienna, Austria)

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    Abstract

    This paper provides sufficient and necessary conditions for the existence of equilibrium pricing rules for monetary utility functions under convex consumption constraints. These utility functions are characterized by the assumption of a fully fungible numeraire asset ("cash"). Each agent's utility is nominally shifted by exactly the amount of cash added to his endowment. We find the individual maximum utility that each agent is eligible for in an equilibrium and provide a game theoretic point of view for the fair allocation of the aggregate utility.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 11 (2008)
    Issue (Month): 03 ()
    Pages: 325-343

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    Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:03:p:325-343

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    Related research

    Keywords: Existence of equilibrium prices; monetary utility functions; Pareto optimal allocation; convex consumption constraints;

    References

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    1. Dana, Rose-Anne & Le Van, Cuong, 2000. "Arbitrage, duality and asset equilibria," Economics Papers from University Paris Dauphine 123456789/6207, Paris Dauphine University.
    2. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172.
    3. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, 01.
    4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean-Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521.
    5. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
    6. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292.
    7. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    8. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
    9. Jeanblanc, Monique & Dana, Rose-Anne, 2003. "Financial Markets in Continuous Time," Economics Papers from University Paris Dauphine 123456789/13604, Paris Dauphine University.
    10. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    11. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
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    Cited by:
    1. Gordan Zitkovic, 2009. "An example of a stochastic equilibrium with incomplete markets," Papers 0906.0208, arXiv.org, revised Jun 2010.
    2. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. repec:hal:journl:halshs-00470670 is not listed on IDEAS
    4. Beatrice Acciaio & Gregor Svindland, 2009. "Optimal risk sharing with different reference probabilities," LSE Research Online Documents on Economics 50119, London School of Economics and Political Science, LSE Library.
    5. Michail Anthropelos, 2012. "Agents' Strategic Behavior in Optimal Risk Sharing," Papers 1206.0384, arXiv.org, revised Mar 2013.
    6. Karl-Theodor Eisele & Michael Kupper, 2013. "Asymptotically Stable Dynamic Risk Assessments," Working Papers of LaRGE Research Center 2013-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    7. Michail Anthropelos & Gordan Žitković, 2010. "Partial equilibria with convex capital requirements: existence, uniqueness and stability," Annals of Finance, Springer, vol. 6(1), pages 107-135, January.
    8. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    9. Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
    10. Didrik Flåm, Sjur, 2012. "Coupled projects, core imputations, and the CAPM," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 170-176.
    11. Acciaio, Beatrice & Svindland, Gregor, 2009. "Optimal risk sharing with different reference probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 426-433, June.
    12. repec:hal:journl:halshs-00281582 is not listed on IDEAS

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