Rational bubbles on assets with a fundamental value

In this paper, we provide a simple framework where a stationary bubble on a dividend-yielding asset portfolio can exist. This bubble is compatible with a positive stationary fundamental value, rather than requiring its collapse in the long run. This result is obtained in an exchange overlapping generations economy with vintage financial assets that depreciate over time. New assets are introduced in each period, ensuring a constant aggregate supply of financial assets. Depreciation introduces a gap between the return of bubbles and the rate at which the dividends are discounted. Since the return on bubbles can be lower than or equal to the growth rate, stationary equilibria can exist with both a positive bubble and a positive fundamental component in the portfolio value. Finally, our framework also allows us to discuss the role of the substitutability between financial assets on the level of bubbles and fundamental values.