Existence of equilibrium with incomplete markets is problematic because demand functions are typically not continuous. Discontinuities occur at prices for which a marketed asset suddenly becomes redundant. We show that this discontinuity disappears if we allow an agent in the economy to introduce a new asset when such redundancies occur. This enables us to prove existence with incomplete markets using a standard path-following argument. Hence, available algorithms for path-following in $\mathbf{R}^K$ can be applied to compute equilibria in the GEI case. We demonstrate this by computing equilibrium for a numerical example.