On equilibrium asset price processes

In this article we derive necessary and sufficient conditionsthat must be satisfied by equilibrium asset price processesin a pure exchange economy. We examine a world in which assetprices follow a diffusion process, asset markets are dynamicallycomplete, all investors maximize their (state-independent) expectedutility of consumption at some future date, and investors havenonrandom exogenous income. We show that it is necessary andsufficient that the coefficients of an equilibrium diffusionprice process satisfy a partial differential equation and aboundary condition. We also examine how the dynamics of assetprices are related to the shape of the representative investor'sutility function through the boundary condition. For example,in a constant-volatility economy, the expected instantaneousreturn of the market portfolio is mean reverting if and onlyif the relative risk aversion of the representative investoris decreasing in terminal wealth.