Extending the Cass Trick

Lionel Boisdeffre
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Lionel 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

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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.

Keywords: asymmetric information; rational expectations; incomplete markets; existence of equilibrium; arbitrage; sequential equilibrium; perfect foresight; équilibre séquentiel; Anticipations parfaites; Existence de l'équilibre; Anticipations rationnelles; Marchés incomplets; Asymétrie d'information (search for similar items in EconPapers)
Date: 2018-09
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Published in 2018

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