On the orientability of the asset equilibrium manifold

Philippe Bich (1)

1 CES - Centre d'économie de la Sorbonne

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.

Mots clés: incomplete markets; equilibria manifold; orientability; index theorem

Domaines: Economies et finances

Philippe Bich. On the orientability of the asset equilibrium manifold. Journal of Mathematical Economics, 2006, 42 (4-5), pp.452-470. ⟨10.1016/j.jmateco.2006.04.004⟩. ⟨halshs-00287677⟩