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The arbitrage pricing theorem with incomplete preferences

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  • Kelsey, David
  • Yalcin, Erkan

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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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 54 (2007)
Issue (Month): 1 (July)
Pages: 90-105

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Handle: RePEc:eee:matsoc:v:54:y:2007:i:1:p:90-105

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. David Kelsey & Frank Milne, 1992. "The arbitrage Pricing Theorem with Non Expected Utility Preferences," Working Papers 866, Queen's University, Department of Economics.
  2. Page, F.H. & Wooders, M.H., 1995. "The partnered core of an economy," Discussion Paper 1995-55, Tilburg University, Center for Economic Research.
  3. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
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  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. 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.
  7. 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.
  8. Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information 0201001, EconWPA.
  9. 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).
  10. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  11. Milne, Frank, 1988. "Arbitrage and Diversification in a General Equilibrium Asset Economy," Econometrica, Econometric Society, vol. 56(4), pages 815-40, July.
  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.
  13. 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.
  14. 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.
  15. Chamberlain, Gary, 1983. "Funds, Factors, and Diversification in Arbitrage Pricing Models," Econometrica, Econometric Society, vol. 51(5), pages 1305-23, September.
  16. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  17. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  18. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  19. 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.
  20. Werner, Jan, 1989. "Equilibrium with incomplete markets without ordered preferences," Journal of Economic Theory, Elsevier, vol. 49(2), pages 379-382, December.
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  24. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
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Cited by:
  1. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
  2. Erkan Yalcin, 2002. "Existence of Equilibrium in Incomplete Markets with Non-Ordered Preferences," GE, Growth, Math methods 0204002, EconWPA.
  3. Naqvi, Nadeem, 2010. "On Non-binary Personal Preferences in Society, Economic Theory and Racial Discrimination," MPRA Paper 21522, University Library of Munich, Germany.
  4. Vantaggi, Barbara, 2010. "Incomplete preferences on conditional random quantities: Representability by conditional previsions," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 104-112, September.

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