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On the orientability of the asset equilibrium manifold

Author

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  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper addresses partly an open question raised in the Handbook of Mathematical Economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S-J is even, where S is the number of states of nature and J the number of assets. This implies, under the same conditions, the orientability of the pseudo-equilibrium manifold. By a standard homotopy argument, it also entails the index theorem for S-J even. A particular case is Momi's result, i.e the index theorem for generic endowments and real asset structures if S-J is even.

Suggested Citation

  • Philippe Bich, 2006. "On the orientability of the asset equilibrium manifold," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00287677, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00287677
    DOI: 10.1016/j.jmateco.2006.04.004
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00287677
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    Cited by:

    1. Momi, Takeshi, 2012. "Failure of the index theorem in an incomplete market economy," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 437-444.

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