Asset price bubbles in Arrow-Debreu and sequential equilibrium

Citation
Kxd. Huang et J. Werner, Asset price bubbles in Arrow-Debreu and sequential equilibrium, ECON THEORY, 15(2), 2000, pp. 253-278
Citations number
17
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Economics
Journal title
ECONOMIC THEORY
ISSN journal
0938-2259 → ACNP
Volume
15
Issue
2
Year of publication
2000
Pages
253 - 278
Database
ISI
SICI code
0938-2259(200003)15:2<253:APBIAA>2.0.ZU;2-7
Abstract
Price bubbles in an Arrow-Debreu equilibrium in an infinite-time economy ar e a manifestation of lack of countable additivity of valuation of assets, I n 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 s equential markets (with no uncertainty) and study the nature of price bubbl es 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 coun tably additive on the set of positive payoffs if and only if there is no Po nzi scheme, provided that there is no restriction on long positions in the assets. In the known examples of equilibrium price bubbles in sequential ma rkets valuation is linear and countably additive. The presence of a price b ubble means that the dividends of an asset can be purchased in sequential m arkets at a cost lower than the asset's price. We present further examples pf equilibrium price bubbles in which valuation is nonlinear, or Linear but not countably additive.