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Portfolio Dominance and Optimality in Infinite Securities Markets

Aliprantis, Charalambos D. and Brown, D. J. and Polyrakis, I. A. and Werner, Jan (1996) Portfolio Dominance and Optimality in Infinite Securities Markets. Social Science Working Paper, 965. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170816-144820990

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Abstract

The most natural way of ordering portfolios is by comparing their payoffs. If a portfolio has a payoff higher than the payoff of another portfolio, then it is greater than the other portfolio. This order is called the portfolio dominance order. An important property that a portfolio dominance order may have is the lattice property. It requires that the supremum and the infimum of any two portfolios are well-defined. The lattice property implies that such portfolio investment strategies as portfolio insurance or hedging an option's payoff are well-defined. The lattice property of the portfolio dominance order plays an important role in the optimality and equilibrium analysis of markets with infinitely many securities with simple (i.e., arbitrary finite) portfolio holdings. If the portfolio dominance order is a lattice order and has a Yudin basis, then optimal portfolio allocations and equilibria in securities markets do exist. A Yudin basis constitutes a system of mutual funds of securities such that trading mutual funds provides the same spanning opportunities, and that the restriction of no short sales of mutual funds is equivalent to the restriction of non-negative wealth.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20170829-160714406Related ItemPublished Version
Alternate Title:Portfolio dominance and optimality in infinite security markets
Additional Information:The research of C. D. Aliprantis and I. A. Polyrakis was partially supported by the 1995 PENED Program of the Ministry of Industry, Energy and Technology of Greece and by the NATO Collaborative Research Grant # 941059. Roko Aliprantis also expresses his deep appreciation for the hospitality provided by the Department of Economics and the Center for Analytic Economics at Cornell University and the Division of Humanities and Social Sciences of the California Institute of Technology where part of the paper was written during his sabbatical leave (January-June, 1996). Published as Aliprantis, Charalambos D., D. J. Brown, I. A. Polyrakis, and Jan Werner. "Portfolio dominance and optimality in infinite security markets." Journal of Mathematical Economics 30, no. 3 (1998): 347-366.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
Ministry of Industry, Energy and Technology (Greece)UNSPECIFIED
North Atlantic Treaty Organization (NATO)941059
Subject Keywords:securities markets, portfolio dominance, equilibrium, Yudin basis
Classification Code:JEL: D41, D52, G11, G22
Record Number:CaltechAUTHORS:20170816-144820990
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170816-144820990
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80505
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:17 Aug 2017 17:12
Last Modified:30 Aug 2017 17:03

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