Equilibrium in Incomplete Markets with Numeraire Assets and Differential Information: An Existence Proof

The paper extends to asymmetric information Geanakoplos-Polemarchakis' (1986) existence theorem for incomplete financial markets with numeraire assets. It builds on a generic existence property of equilibria with real assets and differential information, and applies an asymptotic argument. It presents a two-period pure-exchange economy, with an ex ante uncertainty over the state of nature to be revealed at the second period. Asymmetric information is represented by private sets of states, that each agent is correctly informed to contain the realizable states. Consumers exchange commodities, on spot markets, and securities, on financial markets, which pay off in the same bundle of goods, conditionally on the state of nature to be revealed. Consumers have ordered smooth preferences over consumptions and a perfect foresight of future prices, along Radner (1972). With a different technique of proof, the paper also extends to numeraire assets De Boisdeffre's (2007) existence theorem for nominal assets, which characterizes existence by a no-arbitrage condition.