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

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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

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  • Lionel De Boisdeffre, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Documents de travail du Centre d'Economie de la Sorbonne 21008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:21008
    DOI: 10.1016/j.mathsocsci.2021.01.005
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    File URL: http://mse.univ-paris1.fr/pub/mse/CES2021/21008.pdf
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    Cited by:

    1. de Boisdeffre, Lionel, 2022. "Dropping rational expectations," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 37-46.

    More about this item

    Keywords

    sequential equilibrium; temporary equilibrium; perfect foresight; existence; rational expectations; financial markets; asymmetric information; arbitrage;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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