EXISTENCE OF EQUILIBRIUM WITH INCOMPLETE MARKETS

This paper proves a new fixed-point theorem for establishing generic existence of equilibrium with incomplete markets. The theorem can be stated in two equivalent forms: first as a fixed- point theorem on the Grassmanian of k-dimensional subspaces of Rn.: second as a generalisation of the Borsuk-Ulam theorem. The proof relies on the methods of algebraic topology: geometrically existence follows from the global twisting in the fibres of a naturally induced vector bundle. © 1990.