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Extending the Cass Trick

Author

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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

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 constraint, while all other agents were constrained a la Radner (1972), that is, 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01903494, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01903494
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01903494
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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. 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. 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.
    4. 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.
    5. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    6. 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.
    7. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    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.
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