# SFB 303 Discussion Paper No. A - 444

**Author**: Santos, Manuel S., and Michael Woodford

**Title**: Rational Asset Pricing Bubbles

**Abstract**: This paper is concerned with the conditions under which asset prices in an intertemporal competitive
equilibrium are equal to the present value of the streams of future dividends to which each asset represents a
claim. According to a central result of the theory of finance, this is always true in the case of finite-horizon
economies, as long as there are no restrictions upon transactions other than that associated with possible
incompleteness of the set of securities that are traded. The result is sometimes called " the fundamental theorem
of asset pricing". Here we consider the extent to which such a result continues to be valid in the case of trading
over an infinite horizon. Our framework for analysis in an intertemporal general equilibrium model involving
spot markets for goods and securities at each of a countably infinite sequence of dates. Thus we depart from the
methods of analysis of much of the literature on intertemporal general equilibrium theory, which assumes that
all dated and contingent future goods are traded for one another in a single market. We also allow for potentially
incomplete securities markets that is for cases where there are not even sequentially complete markets in the
sense introduced by Arrow. This results in important complications into the definition of the " fundamental
value" of an asset; it also allows for bubbles in additional types of cases. We allow for incomplete participation
of households in the complete sequence of spot markets, so that our framework can treat standard overlapping
generations models. Finally, we allow for a reasonably general specification of borrowing constraints, to allow
treatment within our framework of both the kinds of infinite-lived households previously considered by
Scheinkman (1977,1988) and Brock (1979,1982) on the one hand, and those considered by Bewley (1980) on the
other.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: November 1993

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