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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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  1. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  2. 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.
  3. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  4. Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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  6. Mukerji, S. & Tallon, J.-M., 1999. "Ambiguity Aversion and Incompleteness of Financial Markets," Papiers d'Economie Mathématique et Applications 1999-28, Université Panthéon-Sorbonne (Paris 1).
  7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  8. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  9. Loomes, Graham & Sugden, Robert, 1987. "Some implications of a more general form of regret theory," Journal of Economic Theory, Elsevier, vol. 41(2), pages 270-287, April.
  10. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  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.
  12. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July.
  13. Page, F.H. & Wooders, M.H., 1995. "The partnered core of an economy," Discussion Paper 1995-55, Tilburg University, Center for Economic Research.
  14. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  15. 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.
  16. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  17. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
  18. Rigotti, L., 1998. "Imprecise Beliefs in a Principal Agent Model," Discussion Paper 1998-128, Tilburg University, Center for Economic Research.
  19. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  20. Milne, Frank, 1976. "Default Risk in a General Equilibrium Asset Economy with Incomplete Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 613-25, October.
  21. 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.
  22. 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.
  23. Werner, Jan, 1989. "Equilibrium with incomplete markets without ordered preferences," Journal of Economic Theory, Elsevier, vol. 49(2), pages 379-382, December.
  24. 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.
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Citations

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Cited by:
  1. Erkan Yalcin, 2002. "Existence of Equilibrium in Incomplete Markets with Non-Ordered Preferences," GE, Growth, Math methods 0204002, EconWPA.
  2. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  3. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.
  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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