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 normalized 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. It is shown that there exists a connected set from an arbitrary price vector to an equilibrium. The path can be followed by a simplicial algorithm for stationary point problems on polytopes. It is argued that this algorithm can be interpreted as originating from a market-maker maximizing the value of excess demand