Intrinsic Bubbles and Mean Reverting Fundamentals

'Intrinsic bubbles' (i.e., bubbles which are related only to fundamentals) are considered in a simple asset pricing model where fundamentals follow an Ornstein-Uhlenbeck process. It is shown that such bubbles imply an explosive path for the expectation of the asset price. It is also shown that the conditional variance of the asset price diverges in finite time. Intrinsic bubbles therefore imply highly nonstationary behaviour for the asset price even when the underlying fundamental to which they are related is stationary.