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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. Kelsey, D. & Milne, F., 1990. "The Arbitrage Pricing Theorem with non Expected Utility Preferences," Papers 217, Australian National University - Department of Economics.
  2. 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.
  3. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  4. Rigotti, L., 1998. "Imprecise Beliefs in a Principal Agent Model," Discussion Paper 1998-128, Tilburg University, Center for Economic Research.
  5. Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information 0201001, EconWPA.
  6. Sujoy Mukerji & Jean-Marc Tallon, 2000. "Ambiguity Aversion and Incompleteness of Financial Markets," Economics Series Working Papers 46, University of Oxford, Department of Economics.
  7. 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.
  8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  9. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  10. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  11. 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.
  12. 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.
  13. Page, F.H. & Holtz Wooders, M., 1995. "The Partenered Core of an Economy," Papers 9555, Tilburg - Center for Economic Research.
  14. Werner,Jan, 1988. "Equilibrium with incomplete markets without ordered preferences," Discussion Paper Serie A 184, University of Bonn, Germany.
  15. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  16. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July.
  17. 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.
  18. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  19. 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.
  20. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  21. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  22. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  23. 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.
  24. 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.
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