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

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  • de Boisdeffre, Lionel

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 be 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 and 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.

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  • de Boisdeffre, Lionel, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 53-62.
    • Handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:53-62
    DOI: 10.1016/j.mathsocsci.2021.01.005
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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.
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    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. Geanakoplos, J. & Polemarchakis, H., 1985. "Existence,regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete," LIDAM Discussion Papers CORE 1985037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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.
    7. Lionel DE BOISDEFFRE, 2015. "Price Revelation and Existence of Financial Equilibrium with Incomplete Markets and Private Beliefs," Working Papers 2014-2015_7, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Mar 2015.
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    9. 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.
    10. Lionel de Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Post-Print halshs-01164142, HAL.
    11. Lionel De Boisdeffre, 2016. "Learning from arbitrage," Post-Print hal-01871266, HAL.
    12. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working Papers hal-02943034, HAL.
    13. Lionel de Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01164142, HAL.
    14. 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.
    15. Lionel De Boisdeffre, 2016. "Learning from arbitrage," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01871266, HAL.
    16. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    17. 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.
    18. 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.
    19. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Documents de travail du Centre d'Economie de la Sorbonne 15037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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    1. de Boisdeffre, Lionel, 2022. "Dropping rational expectations," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 37-46.

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