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Arbitrage and existence of equilibrium in infinite asset markets

Brown, Donald J. and Werner, Jan (1995) Arbitrage and existence of equilibrium in infinite asset markets. Review of Economic Studies, 62 (1). pp. 101-114. ISSN 0034-6527.

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This paper develops a framework for a general equilibrium analysis of asset markets when the number of assets is infinite. Such markets have been studied in the context of asset pricing theories. Our main results concern the existence of an equilibrium. We show that an equilibrium exists if there is a price system under which no investor has an arbitrage opportunity. A similar result has been previously known to hold in finite asset markets. Our extension to infinite assets involves a concept of an arbitrage opportunity which is different from the one used in finite markets. An arbitrage opportunity in finite asset markets is a portfolio that guarantees nonnegative payoff in every event, positive payoff in some event, and has zero price. For the case of infinite asset markets, we introduce a concept of sequential arbitrage opportunity which is a sequence of portfolios which increases an investor's utility indefinitely and has zero price in the limit. We show that a sequential arbitrage opportunity and an arbitrage portfolio are equivalent concepts in finite markets but not in their infinite counterpart.

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Additional Information:© 1995 The Review of Economic Studies, Ltd. First version received January 1992; final version accepted August 1994 (Eds). Acknokvledgements. Support from the National Science Foundation, Deutsche Forschungsgemeinschaft, and Gottfried-Wilhelm-Leibnitz-Förderpreis are gratefully acknowledged. We would like to thank C. D. Aliprantis, O. Burkinshaw, P. Henrotte, Y. Kannai and S. LeRoy for helpful remarks. We have also received helpful comments from the editor and three anonymous referees. In comments on an earlier draft of this paper a referee drew our attention to related recent work by Chichilnisky and Heal (1993b) in which our notion of sequential arbitrage is used to prove the existence of an equilibrium under the restriction that the commodity space is a Sobolev space. Typing assistance of Sally Hattenswits is much appreciated. Formerly SSWP 825.
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Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Subject Keywords:Arbitrage, Consumer economics, Asset markets, Commodities, Financial portfolios, Market equilibrium, Economic theory, Investors, Consumer equilibrium, Consumer prices
Issue or Number:1
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83072
Deposited By: Jacquelyn Bussone
Deposited On:08 Nov 2017 23:18
Last Modified:03 Oct 2019 19:01

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