IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v110y2021icp53-62.html
   My bibliography  Save this article

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

Author

Listed:
  • de Boisdeffre, Lionel

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 be 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 and 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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:53-62
    DOI: 10.1016/j.mathsocsci.2021.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489621000111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2021.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Ho-Mou Wu & Mordecai Kurz, 1996. "Endogenous uncertainty in a general equilibrium model with price contingent contracts (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(3), pages 461-488.
    4. Lionel Boisdeffre, 2007. "No-arbitrage Equilibria with Differential Information: An Existence Proof," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 255-269, May.
    5. 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.
    6. Lionel De Boisdeffre, 2016. "Learning from arbitrage," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01871266, HAL.
    7. 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).
    8. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    9. 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.
    10. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 859-876, October.
    11. 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.
    12. 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.
    13. Lionel DE BOISDEFFRE, 2015. "Price Revelation and Existence of Financial Equilibrium with Incomplete Markets and Private Beliefs," Working Papers 2014-2015_7, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Mar 2015.
    14. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    15. Lionel de Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Post-Print halshs-01164142, HAL.
    16. Lionel De Boisdeffre, 2016. "Learning from arbitrage," Post-Print hal-01871266, HAL.
    17. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working Papers hal-02943034, HAL.
    18. 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.
    19. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Documents de travail du Centre d'Economie de la Sorbonne 15037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Post-Print halshs-03196923, HAL.
    2. de Boisdeffre, Lionel, 2022. "Dropping rational expectations," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 37-46.
    3. Lionel de Boisde¤re, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Post-Print halshs-03196857, HAL.
    4. Lionel De Boisdeffre, 2018. "Equilibrium with Differential Information and Exogenous Beliefs: A Basic Model of Full Existence," Working papers of CATT hal-02141059, HAL.
    5. Lionel de Boisde¤re, 2021. "Dropping Rational Expectations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196897, HAL.
    6. Lionel de Boisdeffre, 2021. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information and Restricted Participation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196923, HAL.
    7. Lionel de Boisde¤re, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03196857, HAL.
    8. Lionel de Boisde¤re, 2021. "Dropping Rational Expectations," Post-Print halshs-03196897, HAL.
    9. Lionel De Boisdeffre, 2018. "Dropping Rational Expectations," Post-Print halshs-01903510, HAL.
    10. Lionel De Boisdeffre, 2018. "Equilibrium with Differential Information and Exogenous Beliefs: A Basic Model of Full Existence," Working Papers hal-02141059, HAL.
    11. Lionel De Boisdeffre, 2018. "Equilibrium with Differential Information and Exogenous Beliefs: A Basic Model of Full Existence," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02141059, HAL.
    12. Lionel de Boisdeffre, 2018. "Sequential equilibrium without rational expectations of prices: A theorem of full existence," Post-Print halshs-01593567, HAL.
    13. Lionel de Boisdeffre, 2018. "Dropping Rational Expectations," Documents de travail du Centre d'Economie de la Sorbonne 18026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Lionel DE BOISDEFFRE, 2018. "Equilibrium with Differential Information and Exogenous Beliefs: A Basic Model of Full Existence," Working Papers 2017-2018_8, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Jun 2018.
    15. Lionel De Boisdeffre, 2018. "Dropping Rational Expectations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01903510, HAL.
    16. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working Papers hal-02943034, HAL.
    17. Lionel De Boisdeffre, 2017. "Sequential Equilibrium without Rational Expectations of Prices: A Theorem of Full Existence," Working papers of CATT hal-02938743, HAL.
    18. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    19. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working papers of CATT hal-02943034, HAL.
    20. Lionel De Boisdeffre, 2018. "Circumventing the Hart Puzzle," Post-Print halshs-01903586, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:53-62. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.