The general equilibrium model with incomplete asset markets provides a unified framework for many problems in finance and macroeconomics. In its simplest version with only two time periods and a single physical commodity the model is ideally suited for the study of problems in cross sectional asset pricing and portfolio theory. In this paper we develop a homotopy algorithm to approximate equilibria in these ''finance economies''. Since the algorithm is tailor made for finance economies, the number of nonlinear equations that has to be solved for, and therefore the computing time,is an order of magnitude smaller than that of existing general purpose algorithms.The algorithm is shown to be generically convergent. We implement the algorithm using HOMPACK. To illustrate its performance, we present various numerical examples and report running times.