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

Aliprantis, Charalambos D., Monteiro, Paulo K. and Tourky, Rabee (2004) Non-marketed options, non-existence of equilibria, and non-linear prices. Journal of Economic Theory, 114 2: 345-357. doi:10.1016/S0022-0531(03)00108-X

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Author Aliprantis, Charalambos D.
Monteiro, Paulo K.
Tourky, Rabee
Title Non-marketed options, non-existence of equilibria, and non-linear prices
Journal name Journal of Economic Theory   Check publisher's open access policy
ISSN 0022-0531
1095-7235
Publication date 2004-02
Sub-type Article (original research)
DOI 10.1016/S0022-0531(03)00108-X
Volume 114
Issue 2
Start page 345
End page 357
Total pages 13
Editor Christian Hellwig
Karl Shell
Place of publication Amsterdam, The Netherlands
Publisher Elsevier
Language eng
Subject 1401 Economic Theory
Formatted abstract
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).
Keyword Existence of equilibrium
Vector lattices
Options
Super-replication
Welfare theorems
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Economics Publications
 
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Created: Fri, 18 Dec 2009, 14:30:55 EST by Elissa Saffery on behalf of School of Economics