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Existence of pseudo-equilibria in a financial economy

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  • Bernard Cornet

    (Department of Economics, The University of Kansas)

  • Philippe Bich

Abstract

This paper proves the existence of a pseudo-equilibrium in a financial economy with incomplete markets in which the agents may have nonordered preferences. We will use a fixed-point-like theorem of [4] that generalizes the results by Hirsch, Magill, Mas-Colell [18] and Husseini, Lasry, Magill [19] to encompass the framework considered by Gale and Mas-Colell ([14],[15]).

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File URL: http://www2.ku.edu/~kuwpaper/2009Papers/200910.pdf
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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200910.

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Length: 15 pages
Date of creation: Dec 2009
Date of revision: Dec 2009
Handle: RePEc:kan:wpaper:200910

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Keywords: Pseudo-equilibrium; incomplete markets; nonordered preferences; fixed-point-like theorems; Grassmann manifold.;

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References

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  1. Smale, S., 1974. "Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 119-127, August.
  2. Smale, S., 1974. "Global analysis and economics v : Pareto theory with constraints," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 213-221, December.
  3. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
  4. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  5. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b04064, Université Panthéon-Sorbonne (Paris 1).
  6. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 41(2), pages 405-416, April.
  7. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
  8. Laura Angeloni & Bernard Cornet, 2005. "Existence Of Financial Equilibria In A Multiperiod Stochastic Economy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200506, University of Kansas, Department of Economics, revised Feb 2005.
  9. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(1), pages 110-119, June.
  10. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, Elsevier, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  11. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
  12. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, Econometric Society, vol. 40(2), pages 289-303, March.
  13. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
  14. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, December.
  15. David Cass, 2006. "Competitive Equilibrium with Incomplete Financial Markets," PIER Working Paper Archive 06-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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Cited by:
  1. Zaier Aouani & Bernard Cornet, 2009. "Existence of financial equilibria with restricted participation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426441, HAL.
  2. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  3. Bernard Cornet & Ramu Gopalan, 2009. "Arbitrage and Equilibrium with Portfolio Constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00441873, HAL.

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