A New Proof of the Index Formula for Incomplete Markets

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Abstract

This paper gives a new proof of the index formula established by [momi, t., 2003. The index theorem for a gei economy when the degree of incompleteness is even. Journal of mathematical economics 39, 273–297] for an economy with incomplete asset markets where the difference between the number of states (ss) and the number of assets (jj) is an even number. The proof uses a single globally defined homotopy function on the asset pseudo-equilibrium manifold connecting the excess demand of a given economy to the individual excess demand of the unconstrained agent. We show that the asset pseudo-equilibrium manifold is orientable if the number s-js-j is even and deduce the index formula from the homotopy invariance theorem for the degree of a map.
Original languageEnglish
Pages (from-to)626-635
Number of pages9
JournalJournal of Mathematical Economics
Volume42
DOIs
Publication statusPublished - 1 Jan 2006

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