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Existence of financial equilibrium with differential information: the no-arbitrage characterization

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  • Lionel De Boisdeffre

    (CATT - Centre d'Analyse Théorique et de Traitement des données économiques - UPPA - Université de Pau et des Pays de l'Adour)

Abstract

In Cornet-De Boisde¤re (J Math Econ 38: 393-410, 2002), we had extended the classical equilibrium and arbitrage concepts of symmetric information to an asymmetric information model dropping Radner's (Econometrica 47: 655-678, 1979) rational expectations' assumption. In Cornet-De Boisdeffre (Econ Theory 38: 287-293, 2009), we showed how agents could infer enough information, in this model, to preclude arbitrage from financial markets. In De Boisdeffre (Econ Theory 31: 255-269, 2007), we extended to that model Cass' (CARESS WP 84-09, 1984) classical existence theorem for nominal assets, by showing the existence of equilibrium was characterized by a general no-arbitrage condition. We now display the same characteristic property for numeraire assets and, thus, extend Geanakoplos-Polemarchakis' (Essays in Honnor of K.J. Arrow, Starr & Starrett ed., Cambridge UP Vol. 3, 65-96, 1986) classical theorem to the asymmetric information setting. Contrasting withRadner's, these results show that symmetric and asymmetric information economies can be embedded into a common model, where they share similar properties.

Suggested Citation

  • Lionel De Boisdeffre, 2015. "Existence of financial equilibrium with differential information: the no-arbitrage characterization," Working Papers hal-02945462, HAL.
    • Handle: RePEc:hal:wpaper:hal-02945462
    Note: View the original document on HAL open archive server: https://univ-pau.hal.science/hal-02945462
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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. 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.
    4. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
    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, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    7. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    8. 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.
    Full references (including those not matched with items on IDEAS)

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