Conditions for bubbles to arise under heterogeneous beliefs

TL;DR

This paper analyzes the conditions under which asset price bubbles can form in markets with heterogeneous investor beliefs, focusing on mean-reverting assets and deriving mathematical conditions for bubble existence.

Contribution

It provides an equivalent condition for bubble formation based on the asset's drift term and characterizes the minimal equilibrium price using differential equations and hypergeometric functions.

Findings

Bubbles depend on the drift term of the asset.

Heterogeneous beliefs do not always lead to bubbles.

The minimal equilibrium price is uniquely characterized by a differential equation.

Abstract

This paper studies the equilibrium price of a continuous time asset traded in a market with heterogeneous investors. We consider a positive mean reverting asset and two groups of investors who have different beliefs on the speed of mean reversion and the mean level. We provide an equivalent condition for bubbles to exist and show that price bubbles may not form even though there are heterogeneous beliefs. This condition is directly related to the drift term of the asset. In addition, we characterize the minimal equilibrium price as a unique $C^2$ solution of a differential equation and express it using confluent hypergeometric functions.