Equilibrium in Incomplete Markets with Differential Information: A Basic Model of Generic Existence

Lionel De Boisdeffre (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 CATT - Centre d'Analyse Théorique et de Traitement des données économiques

The paper demonstrates the generic existence of general equilibria in incomplete 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 financial transfers across periods and states, which are insufficient to span all state contingent claims to value, whatever the spot price to prevail. Under smooth preference and the standard Radner (1972) perfect foresight assumptions, we show that equilibria exist, except for a closed set of measure zero of endowments and securities. This result extends Duffie-Shafer's (1985) in three ways. First, it allows for asymmetric information amongst agents. Second, it holds whenever the equilibrium price is given a fixed norm on each spot market. Third, assets need no longer pay off in commodities, but also in any mix of cash and goods.

Keywords: Sequential Equilibrium; Temporary Equilibrium; Perfect Foresight; Existence; Rational Expectations; Financial Markets; Asymmetric Information; Arbitrage

Domains: Economics and Finance

Lionel De Boisdeffre. Equilibrium in Incomplete Markets with Differential Information: A Basic Model of Generic Existence. 2018. ⟨hal-02141055⟩