A homotopy algorithm and an index theorem for the general equilibrium model with incomplete asset markets

We develop a homotopy algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets (GEI Model). The crucial idea of our approach is to obtain smooth demand functions by introducing penalties on asset sales and gradually lifting this restriction as the algorithm proceeds. The penalties lead to implicit bounds on the optimal asset transactions, eliminating any incentive for agents to inflate their portfolios of assets. Using this algorithm and applying a homotopy invariance theorem, we give what appears to be the first proof of the Index Theorem for the GEI Model for several broad classes of economies generalizing previous results in the literature.