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Refinements to the generic existence of equilibrium in incomplete markets

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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)

Abstract

The paper demonstrates the generic existence of general equilibria in incomplete markets with well behaved price properties. 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, equilibrium is shown to exist, except for a closed set of measure zero of endowments and securities. The proof provides additional arguments and insights to Duffie-Shafer's (1985) on the same subject and refines it in two ways. First, equilibrium in shown to exist generically for any norm values of commodity prices on any spot market, and for any collection of state prices. Second, assets need no longer pay off in commodities, but may in any mix of cash and goods.

Suggested Citation

  • Lionel De Boisdeffre, 2019. "Refinements to the generic existence of equilibrium in incomplete markets," Post-Print halshs-02181033, HAL.
    • Handle: RePEc:hal:journl:halshs-02181033
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02181033
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    References listed on IDEAS

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    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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