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The Arbitrage Pricing Theorem with Incomplete Preferences

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  • David Kelsey
  • Erkan Yalcin

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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File URL: http://128.118.178.162/eps/ge/papers/0401/0401002.pdf
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Bibliographic Info

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
Date of revision:
Handle: RePEc:wpa:wuwpge:0401002

Note: Type of Document - PDF; prepared on Windows Me; pages: 19
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Web page: http://128.118.178.162

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Keywords: Incomplete Preferences; Equilibrium Existence; Arbitrage Pricing Theorem; Knightian Uncertainty;

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References

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  13. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, Econometric Society, vol. 51(5), pages 1305-23, September.
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  15. Kelsey, D. & Milne, F., 1990. "The Arbitrage Pricing Theorem with non Expected Utility Preferences," Papers, Australian National University - Department of Economics 217, Australian National University - Department of Economics.
  16. 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.
  17. 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.
  18. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  19. Rigotti, L., 1998. "Imprecise Beliefs in a Principal Agent Model," Discussion Paper, Tilburg University, Center for Economic Research 1998-128, Tilburg University, Center for Economic Research.
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  21. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  22. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, Econometric Society, vol. 56(4), pages 815-40, July.
  23. 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.
  24. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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Citations

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Cited by:
  1. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.
  2. Erkan Yalcin, 2002. "Existence of Equilibrium in Incomplete Markets with Non-Ordered Preferences," GE, Growth, Math methods, EconWPA 0204002, EconWPA.
  3. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  4. Naqvi, Nadeem, 2010. "On Non-binary Personal Preferences in Society, Economic Theory and Racial Discrimination," MPRA Paper 21522, University Library of Munich, Germany.

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