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

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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 consider a pure exchange financial 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 national 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01164142, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01164142
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01164142
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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. 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.
    3. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    4. John Geanakoplos & Heracles M. Polemarchakis, 1985. "Existence, Regularity, and Constrained Suboptimality of Competitive Allocations When the Asset Market Is Incomplete," Cowles Foundation Discussion Papers 764, Cowles Foundation for Research in Economics, Yale University.
    5. 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.
    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. 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.
    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.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. 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.

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