Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty

TL;DR

This paper demonstrates that under Knightian uncertainty in volatility, the standard implementation of Arrow-Debreu equilibria via continuous trading generally fails unless certain ambiguity-free conditions are met.

Contribution

It identifies the limitations of implementing Arrow-Debreu equilibria under Knightian uncertainty, extending the understanding beyond risk scenarios.

Findings

Implementation fails under general Knightian uncertainty

Implementation is possible if net trades are mean ambiguity-free

Highlights the importance of ambiguity considerations in financial equilibria

Abstract

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are mean ambiguity-free.