Existence of equilibrium and price adjustments in a finance economy with incomplete markets

In this paper the standard two-period general equilibrium model with incomplete financial markets is considered. First, existence of equilibrium is proved using a stationary point argument on the set of no-arbitrage prices. Prices are normalised with respect to the market portfolio. The proof does not use the commonly applied normalization on the unit sphere or truncation of the set of prices. Also a new price adjustment process is proposed. The process generates a path of price vectors from an arbitrary price vector to an equilibrium. The path can be followed by a simplicial algorithm for finding stationary points on polyhedra.