Financial Equilibrium with differential Information: a Theorem of generic Existence

We propose a proof of generic existence of equilibrium in a pure exchange economy, where agents are typically asymmetrically informed, exchange commodities, on spot markets, and securities of all kinds, on incomplete financial markets. The proof does not use Grasmanians, nor differential topology (except Sard's theorem), but good algebraic properties of assets' payoffs, whose spans, generically, never collapse. Then, we show that an economy, where the payoff span cannot fall, admits an equilibrium. As a corollary, we prove the full existence of financial equilibrium for numeraire assets, extending Geanakoplos-Polemarchakis (1986) to the asymmetric information setting. The paper, which still retains Radner's (1972) standard perfect foresight assumption, is also a milestone to prove, in a companion article, the existence of sequential equilibrium when the classical rational expectation assumptions, along Radner (1972, 1979), are dropped jointly, that is, when agents have private characteristics and beliefs and no model to forecast prices.