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Equilibrium theory with satiable and non-ordered preferences

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  • Won, Dong Chul
  • Yannelis, Nicholas C.
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    Abstract

    Abstract This paper investigates the existence of equilibrium in an economy where preferences may be non-ordered and possibly satiable. Remarkably, satiation is allowed to occur only inside the set of feasible and individually rational allocations. One important class of its applications is new developments of asset pricing models where Knightian uncertainty makes preferences incomplete while the absence of a riskless asset makes them satiable. Thus, the result of the paper extends Won et al. (2008) to the case that preferences need be neither complete nor transitive.

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    Bibliographic Info

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

    Volume (Year): 47 (2011)
    Issue (Month): 2 (March)
    Pages: 245-250

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:245-250

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Equilibrium Non-ordered preferences Knightian uncertainty Satiation CAPM Risky assets;

    References

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    1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 12(3), pages 233-245, December.
    2. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 1(3), pages 237-246, December.
    3. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    4. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 37(2), pages 81-94, April.
    5. Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 1999.34, Université Panthéon-Sorbonne (Paris 1).
    6. repec:hal:journl:halshs-00241543 is not listed on IDEAS
    7. Martins-da-Rocha, Victor Filipe & Monteiro, Paulo Klinger, 2007. "Unbounded exchange economies with satiation: how far can we go?," Economics Working Papers (Ensaios Economicos da EPGE) 646, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    8. Allouch, Nizar & Le Van, Cuong, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(9-10), pages 907-918, September.
    9. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, Springer, vol. 4(2), pages 183-195, March.
    10. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, American Economic Association, vol. 91(2), pages 60-66, May.
    11. Page, F.H.Jr. & Wooders, M.H. & Monteiro, P.K., 1999. "Inconsequential Arbitrage," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 561, University of Warwick, Department of Economics.
    12. Shafer, Wayne J., 1976. "Equilibrium in economies without ordered preferences or free disposal," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 3(2), pages 135-137, July.
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    14. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
    15. Chichilnisky, Graciela, 1995. "Limited Arbitrage Is Necessary and Sufficient for the Existence of a Competitive Equilibrium with or without Short Sales," Economic Theory, Springer, Springer, vol. 5(1), pages 79-108, January.
    16. 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.
    17. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 1169-74, July.
    18. H. Henry Cao & Tan Wang & Harold H. Zhang, 2005. "Model Uncertainty, Limited Market Participation, and Asset Prices," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 18(4), pages 1219-1251.
    19. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 2(1), pages 9-15, March.
    20. Won, Dong Chul & Yannelis, Nicholas C., 2008. "Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(11), pages 1266-1283, December.
    21. Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(2), pages 315-24, April.
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    Cited by:
    1. Pınar, Mustafa Ç., 2014. "Equilibrium in an ambiguity-averse mean–variance investors market," European Journal of Operational Research, Elsevier, Elsevier, vol. 237(3), pages 957-965.
    2. Miyazaki, Kentaro & Takekuma, Shin-Ichi, 2013. "A note on the existence of Walras equilibrium in irreducible economies with satiable and non-ordered preferences," Discussion Papers, Graduate School of Economics, Hitotsubashi University 2013-14, Graduate School of Economics, Hitotsubashi University.
    3. Miyazaki, Kentaro & Takekuma, Shin-Ichi, 2012. "On the existence of Walras equilibrium in irreducible economies with satiable and non-ordered preferences," Discussion Papers, Graduate School of Economics, Hitotsubashi University 2012-05, Graduate School of Economics, Hitotsubashi University.

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