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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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    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000383
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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. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
    2. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series qt6m42r5rr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    3. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
    4. Allouch, Nizar & Le Van, Cuong, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 907-918, September.
    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 1999.34, Université Panthéon-Sorbonne (Paris 1).
    6. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    7. Mas-Colell, Andrew, 1974. "An equilibrium existence theorem without complete or transitive preferences," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 237-246, December.
    8. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-74, July.
    9. Chichilnisky, Graciela, 1995. "Limited Arbitrage Is Necessary and Sufficient for the Existence of a Competitive Equilibrium with or without Short Sales," Economic Theory, Springer, vol. 5(1), pages 79-108, January.
    10. Page, F.H.Jr. & Wooders, M.H. & Monteiro, P.K., 1999. "Inconsequential Arbitrage," The Warwick Economics Research Paper Series (TWERPS) 561, University of Warwick, Department of Economics.
    11. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    12. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
    13. Nielsen, Lars Tyge, 1990. "Equilibrium in CAPM without a Riskless Asset," Review of Economic Studies, Wiley Blackwell, vol. 57(2), pages 315-24, April.
    14. Martins-da-Rocha, V. Filipe & Monteiro, Paulo K., 2009. "Unbounded exchange economies with satiation: How far can we go?," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 465-478, July.
    15. Nizar Allouch & Cuong Le Van & Frank H. Page, 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00096040, HAL.
    16. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    17. 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, vol. 44(11), pages 1266-1283, December.
    18. Shafer, Wayne J., 1976. "Equilibrium in economies without ordered preferences or free disposal," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 135-137, July.
    19. 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, vol. 18(4), pages 1219-1251.
    20. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
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    Cited by:
    1. Miyazaki, Kentaro & Takekuma, Shin-Ichi, 2012. "On the existence of Walras equilibrium in irreducible economies with satiable and non-ordered preferences," Discussion Papers 2012-05, Graduate School of Economics, Hitotsubashi University.
    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 2013-14, Graduate School of Economics, Hitotsubashi University.

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