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Equilibrium in incomplete markets with differential information: A basic model of generic existence

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  • Lionel de Boisde¤re

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

The paper demonstrates the generic existence of general equilibria in incomplete financial markets with asymmetric information. The economy has two periods and an ex ante uncertainty over the state of nature to be revealed at the second period. Securities pay off in cash or commodities at the second period, conditionally on the state of nature to br revealed. They permit transfers across periods and states, which are typically insufficient to span all state contingent claims to value, whatever the spot price to prevail. Under the standard smooth preference and perfect foresight assumptions, the paper shows that equilibria exist, except for a closed set of measure zero of securities and endowments. This theorem generalizes Duffie-Shafer's (1985) to arbitrary financial and information structures. The equilibrium prices are consistent with any collection of state prices and norm values on spot markets. This refinement permits to extend to asymmetric information Cass' (1984) theorem that any collection of state prices supports an equilibrium on purely financial markets.

Suggested Citation

  • Lionel de Boisde¤re, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Post-Print halshs-03196857, HAL.
    • Handle: RePEc:hal:journl:halshs-03196857
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03196857
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    References listed on IDEAS

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    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    2. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    3. Ho-Mou Wu & Mordecai Kurz, 1996. "Endogenous uncertainty in a general equilibrium model with price contingent contracts (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 461-488.
    4. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    5. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    6. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    7. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 859-876, October.
    8. 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.
    9. 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.
    10. 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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