Bubbles as payoffs at infinity

Summary We define rational bubbles to be securities with payoffs occurring in the infinitely distant future and investigate the behavior of bubbles values. We extend our analysis to a setting of uncertainty. In an infinite horizon arbitrage-free model of asset prices, we interpret the money market account as the value of a particular bubble; a similar interpretation holds for other assets related to the state-price deflator and to payoffs on bonds maturing in the distant future. We present three applications of this characterization of bubbles.This paper was circulated under the title Stochastic bubbles in Markov economies. We acknowledge with gratitude numerous conversations with Mark Fisher, the editorial advice of David Levine and the useful comments of anonymous referees. This paper should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or its staff.