The most natural way of ordering portfolios is by comparing their payoffs. A portfolio with payoff higher than the payoff of another portfolio is greater in the sense of portfolio dominance than that other portfolio. Portfolio dominance is a lattice order if the supremum and the infimum of any two portfolios are well-defined. We study security markets with infinitely many securities and arbitrary finite portfolio holdings. If portfolio dominance order is a lattice order and has a Yudin basis, then optimal portfolio allocations and equilibria in security markets do exist.
Bibliographical noteFunding 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 to June, 1996). J. Werner acknowledges the financial support of the Deutsche Forschungsgemainschaft, SFB 303, University of Bonn during his sabbatical leave August 1995 to July 1996.
- Portfolio dominance
- Security markets
- Yudin basis