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When Heterogeneous Beliefs Produce Asset Price Bubbles

Article arXiv papers · Author: Seunghyun Lee et al.
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Summary

The paper analyzes equilibrium pricing for a positive, mean-reverting asset in continuous time when investors differ in their beliefs about the speed of mean reversion and the asset’s long-run mean. Its central result is a condition for the existence of price bubbles, showing that disagreement among investors alone does not guarantee a bubble. The condition is tied directly to the asset’s drift.

The paper also characterizes the minimal equilibrium price as the unique twice-differentiable solution to a differential equation and gives an expression using confluent hypergeometric functions. This is a theoretical analysis rather than an empirical trading study: the provided description offers no data, estimated parameters, or strategy tests. Its conclusions therefore depend on the specified asset dynamics and investor belief structure, and the summary does not establish how they apply to other market settings.

Key ideas

  • The model considers continuous-time pricing of a positive, mean-reverting asset.
  • Investors hold different beliefs about mean-reversion speed and the long-run mean.
  • Heterogeneous beliefs do not necessarily produce a price bubble.
  • The bubble condition is linked to the asset’s drift.
  • The minimal equilibrium price is characterized by a differential equation and confluent hypergeometric functions.

Tags

Mean reversionStatisticsMulti-asset
Full text
# Conditions for bubbles to arise under heterogeneous beliefs


# Conditions for bubbles to arise under heterogeneous beliefs









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.