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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.

Suggested Citation

  • David Kelsey & Erkan Yalcin, 2004. "The Arbitrage Pricing Theorem with Incomplete Preferences," GE, Growth, Math methods 0401002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpge:0401002
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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, University Library of Munich, Germany.
    2. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    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.
    5. Tian, Dejian & Tian, Weidong, 2014. "Optimal risk-sharing under mutually singular beliefs," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 41-49.

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    More about this item

    Keywords

    Incomplete Preferences; Equilibrium Existence; Arbitrage Pricing Theorem; Knightian Uncertainty;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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