Market crashes, speculation and learning in financial markets

TLDR: In this paper, the authors extend Sandroni's result by showing that the conjecture is generically true for economies with complete markets and show that, for almost every such economy, if conditional beliefs eventually become correct along a path of events, equilibrium prices of assets traded along this path converge to rational expectations equilibria in the sup-norm.

Abstract: A natural conjecture is that if agents’ beliefs are almost correct then equilibrium prices should be close to rational expectations prices. Sandroni (J Econ Theory 82:1–18, 1998) gives a counterexample in an economy with sunspots and complete markets. We extend Sandroni’s result by showing that the conjecture is generically true for economies with complete markets. We consider a standard General Equilibrium model with large but finite horizon and complete markets. We show that, for almost every such economy, if conditional beliefs eventually become correct along a path of events then equilibrium prices of assets traded along this path converge to rational expectations equilibria in the sup-norm. Moreover, we establish that, generically, there exist along any such path local diffeomorphisms between individual beliefs and equilibrium prices.