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- Title
Asset price bubbles in Arrow-Debreu and sequential equilibrium.
- Authors
Huang, Kevin X. D.; Werner, Jan
- Abstract
Price bubbles in an Arrow-Debreu equilibrium in an infinite-time economy are a manifestation of lack of countable additivity of valuation of assets. In contrast, the known examples of price bubbles in a sequential equilibrium in infinite time cannot be attributed to the lack of countable additivity of valuation. In this paper we develop a theory of valuation of assets in sequential markets (with no uncertainty) and study the nature of price bubbles in light of this theory We define a payoff pricing operator that maps a sequence of payoffs to the minimum cost of an asset holding strategy that generates it We show that the payoff pricing functional is linear and countably additive on the set of positive payoffs if and only if there is no Ponzi scheme, provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential markets valuation is linear and countably additive. The presence of a price bubble means that the dividends of an asset can be purchased in sequential markets at a cost lower than the asset's price. We present further examples of equilibrium price bubbles in which valuation is nonlinear, or linear but not countably additive.
- Subjects
ECONOMIC equilibrium; ECONOMIC models; PRICING; VALUATION; MATHEMATICAL models
- Publication
Economic Theory, 2000, Vol 15, Issue 2, p253
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/s001990050012