Asset price bubbles from heterogeneous beliefs about mean reversion rates

Harrison and Kreps showed in 1978 how the heterogeneity of investor beliefs can drive speculation, leading the price of an asset to exceed its intrinsic value. By focusing on an extremely simple market model—a finite-state Markov chain—the analysis of Harrison and Kreps achieved great clarity but limited realism. Here we achieve similar clarity with greater realism, by considering an asset whose dividend rate is a mean-reverting stochastic process. Our investors agree on the volatility, but have different beliefs about the mean reversion rate. We determine the minimum equilibrium price explicitly; in addition, we characterize it as the unique classical solution of a certain linear differential equation. Our example shows, in a simple and transparent manner, how heterogeneous beliefs about the mean reversion rate can lead to everlasting speculation and a permanent “price bubble.”