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Equilibrium in Incomplete Markets with Differential Information: A Basic Model of Generic Existence

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  • Lionel De Boisdeffre

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour)

Abstract

The paper demonstrates the generic existence of general equilibria in incomplete 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 be revealed. They permit financial transfers across periods and states, which are insufficient to span all state contingent claims to value, whatever the spot price to prevail. Under smooth preference and the standard Radner (1972) perfect foresight assumptions, we show that equilibria exist, except for a closed set of measure zero of endowments and securities. This result extends Duffie-Shafer's (1985) in three ways. First, it allows for asymmetric information amongst agents. Second, it holds whenever the equilibrium price is given a fixed norm on each spot market. Third, assets need no longer pay off in commodities, but also in any mix of cash and goods.

Suggested Citation

  • Lionel De Boisdeffre, 2018. "Equilibrium in Incomplete Markets with Differential Information: A Basic Model of Generic Existence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02141055, HAL.
    • Handle: RePEc:hal:cesptp:hal-02141055
    Note: View the original document on HAL open archive server: https://univ-pau.hal.science/hal-02141055
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    References listed on IDEAS

    as
    1. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    2. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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