IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/18025.html
   My bibliography  Save this paper

Extending the Cass Trick

Author

Abstract

In a celebrated 1984 paper, David Cass provided an existence theorem for financial equilibria in incomplete markets with exogenous yields. The theorem showed that, when agents had symmetric information and ordered preferences, equilibria existed on purely financial markets and could be supported by any collection of state prices. This theorem built on the so-called "Cass trick", along which one agent in the economy had an Arrow-Debreu budget set, with one single budget constraint, while all other agents were constrained à la Radner (1972), that is, in every state of nature, given the financial transfers that the asset market permitted. The current paper extends Cass' theorem and the Cass trick to asymmetric information and non-ordered preferences. It shows that any collection of individual state prices under asymmetric information supports an equilibrium, provided one agent had full information. If the latter condition fails, the Cass trick cannot apply. A weaker result holds, namely equilibrium exists under the no-arbitrage condition

Suggested Citation

  • Lionel de Boisdeffre, 2018. "Extending the Cass Trick," Documents de travail du Centre d'Economie de la Sorbonne 18025, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:18025
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2018/18025.pdf
    Download Restriction: no
    ---><---

    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. 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.
    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. 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. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    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. 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.
    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)

    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. 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.
    3. Lionel De Boisdeffre, 2018. "Extending the Cass Trick," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01903494, HAL.
    4. Lionel De Boisdeffre, 2018. "Extending the Cass Trick," Post-Print halshs-01903494, HAL.
    5. Lionel De Boisdeffre, 2019. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02180836, HAL.
    6. Lionel De Boisdeffre, 2019. "Dropping the Cass Trick and Extending Cass' Theorem to Asymmetric Information," Post-Print halshs-02180836, HAL.
    7. Lionel DE BOISDEFFRE, 2015. "Existence of financial equilibrium with differential information: the no-arbitrage characterization," Working Papers 2015-2016_5, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Nov 2015.
    8. Lionel De Boisdeffre, 2015. "Existence of financial equilibrium with differential information: the no-arbitrage characterization," Working Papers hal-02945462, HAL.
    9. Lionel De Boisdeffre, 2018. "Circumventing the Hart Puzzle," Post-Print halshs-01903586, HAL.
    10. Lionel De Boisdeffre, 2018. "Circumventing the Hart Puzzle," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01903586, HAL.
    11. Lionel De Boisdeffre, 2015. "Existence of financial equilibrium with differential information: the no-arbitrage characterization," Working papers of CATT hal-02945462, HAL.
    12. Lionel de Boisdeffre, 2018. "Circumventing the Hart Puzzle," Documents de travail du Centre d'Economie de la Sorbonne 18027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    13. Lionel de Boisdeffre, 2018. "Sequential equilibrium without rational expectations of prices: A theorem of full existence," Post-Print halshs-01593567, HAL.
    14. Lionel de Boisdeffre, 2013. "Price revelation and existence of equilibrium in a private belief economy," Post-Print halshs-01053471, HAL.
    15. Lionel DE BOISDEFFRE, 2015. "Learning from arbitrage," Working Papers 2015-2016_2, CATT - UPPA - Université de Pau et des Pays de l'Adour, revised Sep 2015.
    16. de Boisdeffre, Lionel, 2022. "Dropping rational expectations," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 37-46.
    17. Lionel de Boisde¤re, 2021. "Equilibrium in incomplete markets with differential information: A basic model of generic existence," Post-Print halshs-03196857, HAL.
    18. Lionel De Boisdeffre, 2015. "Price revelation and existence of financial equilibrium with incomplete markets and private beliefs," Working papers of CATT hal-02943034, HAL.
    19. 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.
    20. Lionel de Boisdeffre, 2017. "Sequential equilibrium without rational expectations of prices: A theorem of full existence," Documents de travail du Centre d'Economie de la Sorbonne 17036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    Keywords

    sequential equilibrium; perfect foresight; existence of equilibrium; rational expectations; incomplete markets; asymmetric information; arbitrage;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:mse:cesdoc:18025. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.