Non-marketed options, non-existence of equilibria, and non-linear prices

• 成果类型: Article
• 署名作者: Aliprantis, CD; Monteiro, PK; Tourky, R
• 署名单位: University of Melbourne; Getulio Vargas Foundation; Purdue University System; Purdue University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/S0022-0531(03)00108-X
• 发表日期: 2004
• 页码: 345-357
• 关键词: existence of equilibrium; vector lattices; options; super-replication; welfare theorems

摘要

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional. The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails. Our example has important finite- as well as infinite-dimensional implications. It is also an example of a well behaved economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001). (C) 2003 Elsevier Science (USA). All rights reserved.