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The Arbitrage Pricing Theorem with Incomplete Preferences

  • David Kelsey
  • Erkan Yalcin

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://econwpa.repec.org/eps/ge/papers/0401/0401002.pdf
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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
Date of revision:
Handle: RePEc:wpa:wuwpge:0401002
Note: Type of Document - PDF; prepared on Windows Me; pages: 19
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  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. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
  4. Page Jr., F.H. & Wooders, M.H., 1995. "The partnered core of an economy," Discussion Paper 1995-55, Tilburg University, Center for Economic Research.
  5. 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.
  6. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  7. Rigotti, L., 1998. "Imprecise Beliefs in a Principal Agent Model," Discussion Paper 1998-128, Tilburg University, Center for Economic Research.
  8. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  9. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  10. 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.
  11. Werner,Jan, 1988. "Equilibrium with incomplete markets without ordered preferences," Discussion Paper Serie A 184, University of Bonn, Germany.
  12. Sujoy Mukerji & Jean-Marc Tallon, 2000. "Ambiguity Aversion and Incompleteness of Financial Markets," Economics Series Working Papers 46, University of Oxford, Department of Economics.
  13. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, 01.
  14. 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.
  15. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  16. 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.
  17. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  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. 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.
  20. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  21. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  22. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July.
  23. 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.
  24. 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.
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