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Equilibrium analysis in financial markets with countably many securities

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  • Aliprantis, C. D.
  • Florenzano, M.
  • Martins-da-Rocha, V. F.
  • Tourky, R.

Abstract

An F-cone is a pointed and generating convex cone of a real vector space that is the union of a countable family of finite dimensional polyedral convex cones such that each of which is an extremel subset of the subsequent one. In this paper, we study securities markets with countably many securities and arbitrary finite portfolio holdings. Moreover, we assume that each investor is constrained to have a non-negative end-of-period wealth. If, under the portfolio dominance order, the positive cone of the portfolio space is an F-cone, then Edgeworth allocations and non-trivial quasi-equilibria exist. This result extend the case where, as in Aliprantis et al.[JME 30 (1998a) 347-366], the positive cone is a Yudin cone.
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Suggested Citation

  • Aliprantis, C. D. & Florenzano, M. & Martins-da-Rocha, V. F. & Tourky, R., 2004. "Equilibrium analysis in financial markets with countably many securities," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 683-699, September.
    • Handle: RePEc:eee:mateco:v:40:y:2004:i:6:p:683-699
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    1. Donald J. Brown & Jan Werner, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 101-114.
    2. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2004. "General equilibrium analysis in ordered topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 247-269, June.
    3. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-1137, September.
    4. Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, vol. 78(2), pages 321-328, February.
    5. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    6. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    7. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
    8. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    9. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
    10. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    11. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
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    Cited by:

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    2. Bloise, Gaetano & Calciano, Filippo L., 2008. "A characterization of inefficiency in stochastic overlapping generations economies," Journal of Economic Theory, Elsevier, vol. 143(1), pages 442-468, November.
    3. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    4. Ellen Fukuda & L. Graña Drummond, 2013. "Inexact projected gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 473-493, April.
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    6. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
    7. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.

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    More about this item

    JEL classification:

    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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