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Portfolio Dominance and Optimality in Infinite Security Markets

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  • Aliprantis, C. D.
  • D. J. Brown
  • I. A. Polyrakis
  • J. Werner

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. Yudin basis constitutes a system of mutual funds of securities such that trading mutual funds provides spanning opportunities, and that the restriction of no short sales of mutual funds is equivalent to the restriction of non-negative wealth.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 383.

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Length: pages
Date of creation: Jul 1996
Date of revision:
Handle: RePEc:bon:bonsfb:383

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

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Keywords: securities markets; portfolio dominance; equilibrium; Yudin basis;

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  1. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
  2. Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, vol. 59(2), pages 364-384, April.
  3. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
  4. Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 101-14, January.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  6. Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, vol. 75(1), pages 89-103, July.
  7. Milne, Frank, 1987. "The induced preference approach to arbitrage and diversification arguments in finance," European Economic Review, Elsevier, vol. 31(1-2), pages 235-245.
  8. Milne, Frank, 1976. "Default Risk in a General Equilibrium Asset Economy with Incomplete Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 613-25, October.
  9. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  10. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  11. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 31(1), pages 170-175, October.
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