Arbitrage and price revelation with private beliefs
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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- 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.
- 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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"Elimination Of Arbitrage States In Asymmetric Information Models,"
WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS
200504, University of Kansas, Department of Economics, revised Feb 2005.
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- 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.
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