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Price revelation and existence of financial equilibrium with incomplete markets and private beliefs

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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

We consider a pure exchange nancial economy, where rational agents, possibly asymmetrically informed, forecast prices privately, with no model of how they are determined. Therefore, agents face both 'exogenous uncertainty', on the future state of nature, and 'endogenous uncertainty', on the future price. At a sequential equilibrium, all consumers expect the 'true' price as a possible outcome and elect optimal strategies at the first period, which clear on all markets, ex post. The paper's purpose is twofold. First, it defines no-arbitrage prices, which comprise all equilibrium prices, and displays their revealing properties. Second, it shows, under mild conditions, that a sequential equilibrium always exists in this model, whatever agents' prior beliefs or the financial structure. This outcome suggests that standard existence problems, which followed Hart (1975) and Radner (1979), stem from the rational expectation and perfect foresight assumptions of the classical model.

Suggested Citation

  • Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working papers of CATT hal-02943034, HAL.
    • Handle: RePEc:hal:wpcatt:hal-02943034
    Note: View the original document on HAL open archive server: https://hal-univ-pau.archives-ouvertes.fr/hal-02943034
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    References listed on IDEAS

    as
    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. Busch, Lutz-Alexander & Govindan, Srihari, 2004. "Robust nonexistence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 641-645, September.
    5. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    6. 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.
    7. 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.
    8. Momi, Takeshi, 2001. "Non-existence of equilibrium in an incomplete stock market economy," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 41-70, February.
    9. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    10. 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.
    11. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
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