Portfolio dominance and optimality in infinite security markets
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 30 (1998)
Issue (Month): 3 (October)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jmateco
Other versions of this item:
- Aliprantis, C. D. & D. J. Brown & I. A. Polyrakis & J. Werner, 1996. "Portfolio Dominance and Optimality in Infinite Security Markets," Discussion Paper Serie B, University of Bonn, Germany 383, University of Bonn, Germany.
- D41 - Microeconomics - - Market Structure and Pricing - - - Perfect Competition
- D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(3), pages 341-360, December.
- Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
- Dana, R.A. & Le Van, C. & Magnien, F., 1994.
"General equilibrium in asset markets with or without short-selling,"
Discussion Paper, Tilburg University, Center for Economic Research
1994-92, Tilburg University, Center for Economic Research.
- Dana, R.A. & Le Van, C. & Magnien, F., 1994. "General Equilibrium in Asset Markets with or without Short-Selling," Papers, Tilburg - Center for Economic Research 9492, Tilburg - Center for Economic Research.
- Werner, Jan, 1997. "Diversification and Equilibrium in Securities Markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 75(1), pages 89-103, July.
- Brown, Donald & Werner, Jan, 1993.
"Arbitrage and Existence of Equilibrium in Infinite Asset Markets,"
Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences
825, California Institute of Technology, Division of the Humanities and Social Sciences.
- Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 62(1), pages 101-14, January.
- Brown,Donald & Werner,Jan, 1991. "Arbitrage and existence of equilibrium in infinite asset markets," Discussion Paper Serie A, University of Bonn, Germany 344, University of Bonn, Germany.
- Brown, D.J. & Werner, J., 1992. "Arbitrage and Existence of Equilibrium in Finite Asset Markets," Papers, Stanford - Institute for Thoretical Economics 43, Stanford - Institute for Thoretical Economics.
- Milne, Frank, 1987. "The induced preference approach to arbitrage and diversification arguments in finance," European Economic Review, Elsevier, Elsevier, vol. 31(1-2), pages 235-245.
- Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 20(1), pages 137-152.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
- 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 613-25, October.
- Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(2), pages 364-384, April.
- Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, Elsevier, vol. 34(1), pages 13-31, October.
- Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
- Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 31(1), pages 170-175, October.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.