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Financial Equilibrium with differential Information: a Theorem 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

We propose a proof of generic existence of equilibrium in a pure exchange economy, where agents are typically asymmetrically informed, exchange commodities, on spot markets, and securities of all kinds, on incomplete financial markets. The proof does not use Grasmanians, nor differential topology (except Sard's theorem), but good algebraic properties of assets' payoffs, whose spans, generically, never collapse. Then, we show that an economy, where the payoff span cannot fall, admits an equilibrium. As a corollary, we prove the full existence of financial equilibrium for numeraire assets, extending Geanakoplos-Polemarchakis (1986) to the asymmetric information setting. The paper, which still retains Radner's (1972) standard perfect foresight assumption, is also a milestone to prove, in a companion article, the existence of sequential equilibrium when the classical rational expectation assumptions, along Radner (1972, 1979), are dropped jointly, that is, when agents have private characteristics and beliefs and no model to forecast prices.

Suggested Citation

  • Lionel De Boisdeffre, 2017. "Financial Equilibrium with differential Information: a Theorem of generic Existence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01871571, HAL.
  • Handle: RePEc:hal:cesptp:hal-01871571
    Note: View the original document on HAL open archive server: https://univ-pau.hal.science/hal-01871571
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    References listed on IDEAS

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    1. 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.
    2. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    3. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
    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. 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.
    6. 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.
    7. 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.
    8. 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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