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Failure of the index theorem in an incomplete market economy

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  • Momi, Takeshi

Abstract

Recently, it was proved that the index of an economy with incomplete real asset markets is typically +1 when the degree of incompleteness, which is defined as the difference between the number of states and the number of securities, is an even number. This paper considers the case where the degree of incompleteness is an odd number and proves that any odd number can be realized as the index of such an economy.

Suggested Citation

  • Momi, Takeshi, 2012. "Failure of the index theorem in an incomplete market economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 437-444.
  • Handle: RePEc:eee:mateco:v:48:y:2012:i:6:p:437-444
    DOI: 10.1016/j.jmateco.2012.07.004
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    References listed on IDEAS

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    1. Momi, Takeshi, 2010. "Excess demand function around critical prices in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 293-302, May.
    2. repec:dau:papers:123456789/6111 is not listed on IDEAS
    3. Bottazzi, Jean-Marc & Hens, Thorsten, 1996. "Excess Demand Functions and Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 68(1), pages 49-63, January.
    4. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
    5. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Philippe Bich, 2006. "On the orientability of the asset equilibrium manifold," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00287677, HAL.
    8. Geanakoplos, J D & Polemarchakis, H M, 1980. "On the Disaggregation of Excess Demand Functions," Econometrica, Econometric Society, vol. 48(2), pages 315-331, March.
    9. Momi, Takeshi, 2003. "The index theorem for a GEI economy when the degree of incompleteness is even," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 273-297, June.
    10. Dierker, Egbert, 1972. "Two Remarks on the Number of Equilibria of an Economy," Econometrica, Econometric Society, vol. 40(5), pages 951-953, September.
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    Keywords

    Incomplete market; Index theorem; Homotopy;

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