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The Arbitrage Pricing Theorem with Incomplete Preferences

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Author Info
David Kelsey
Erkan Yalcin

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Abstract

This paper proves existence of equilibrium and the arbitrage pricing theorem for an asset exchange economy, where the individual's preferences may be incomplete or intransitive. This extends existing results to a more general set of individual preferences. We also prove the arbitrage pricing theorem for a theory of choice under uncertainty by Bewley [1986]. These preferences model Knightian uncertainty by allowing for the possibility that preferences are incomplete.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0401002.

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Length: 19 pages
Date of creation: 22 Jan 2004
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Handle: RePEc:wpa:wuwpge:0401002

Note: Type of Document - PDF; prepared on Windows Me; pages: 19
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Related research
Keywords: Incomplete Preferences; Equilibrium Existence; Arbitrage Pricing Theorem; Knightian Uncertainty;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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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.:
  1. Haller, Hans, 1991. "Corporate Production and Shareholder Cooperation under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(4), pages 823-42, November. [Downloadable!] (restricted)
  2. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October. [Downloadable!] (restricted)
  3. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November. [Downloadable!] (restricted)
  6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December. [Downloadable!] (restricted)
  8. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June. [Downloadable!] (restricted)
  9. Wooders, M., 1994. "The Partnered Core of an Economy," UFAE and IAE Working Papers 279.94, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    Other versions:
  10. Kelsey David & Milne Frank, 1995. "The Arbitrage Pricing Theorem with Non-expected Utility Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 557-574, April. [Downloadable!] (restricted)
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  11. Bergstrom, Theodore C. & Parks, Robert P. & Rader, Trout, 1976. "Preferences which have open graphs," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 265-268, December. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
  13. Rigotti, L., 1998. "Imprecise beliefs in a principal agent model," Discussion Paper 128, Tilburg University, Center for Economic Research. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Erkan Yalcin, 2002. "Existence of Equilibrium in Incomplete Markets with Non-Ordered Preferences," GE, Growth, Math methods 0204002, EconWPA. [Downloadable!]
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