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Arbitrage and price revelation with private beliefs

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    Abstract

    We extend the Cornet-de Boisdeffre (2002-2009) asymmetric information finite dimensional model to a more general setting, where agents may forecast prices with some private uncertainty. This new model drops both Radner's (1972-1979) classical, but restrictive, assumptions of rational expectations and perfect foresight. It deals with sequential financial equilibrium, when agents, unaware of how equilibrium prices or quantities are determined, are prone to uncertainty between - possibly uncountable - forecasts. Under perfect foresight, the extended model coincides with Cornet-de Boisdeffre's (2002-2009). Yet, when anticipations are private, we argue any element of a typically uncountable ‘minimum uncertainty set’ may prevail as an equilibrium price tomorrow. This outcome is inconsistent with perfect foresight and appeals for a broader definition of sequential equilibrium, which we propose hereafter. By standard techniques, we embed and extend Cornet-de Boisdeffre's (2002-2009) results, to the infinite dimensional model. The aim is to lay foundations for another paper, showing that the concept of sequential equilibrium we propose may solve the classical existence problems of the perfect foresight model, following Hart (1974).

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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2012/12053.pdf
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    Bibliographic Info

    Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12053.

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    Length: 28 pages
    Date of creation: Jul 2012
    Date of revision:
    Handle: RePEc:mse:cesdoc:12053

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    Keywords: Sequential equilibrium; temporary equilibrium; perfect foresight; expectations; incomplete markets; asymmetric information; arbitrage.;

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    1. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    2. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-23, November.
    3. repec:hal:cesptp:halshs-00441895 is not listed on IDEAS
    4. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    5. Bernard Cornet & Lionel D Boisdeffre, 2009. "Elimination of Arbitrage States in Asymmetric Information Models," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200912, University of Kansas, Department of Economics, revised Dec 2009.
    6. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 31(1), pages 170-175, October.
    7. Yves Balasko, 2003. "Temporary financial equilibrium," Economic Theory, Springer, vol. 21(1), pages 1-18, 01.
    8. Grandmont, Jean-Michel, 1977. "Temporary General Equilibrium Theory," Econometrica, Econometric Society, vol. 45(3), pages 535-72, April.
    9. Cornet, Bernard & De Boisdeffre, Lionel, 2002. "Arbitrage and price revelation with asymmetric information and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 393-410, December.
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