On Equilibrium Asset Price Processes

In this article we derive necessary and sufficient conditions that must be satisfied by equilibrium asset price processes in apure exchange economy. We examine a world in which asset prices follow a diffusion process, asset markets are dynamically complete, all investors maximize their (state-independent) expected utility of consumption at some future date, and investors have nonrandom exogenous income. We show that it is necessary and suffcient that the coefficients of an equilibrium diffusion price process satisfy a partial differential equation and a boundary condition. We also examine how the dynamics of asset prices are related to the shape of the representative investor's utility function through the boundary condition. For example, in a constant-volatility economy, the expected instantaneous return of the market portfolio is mean reverting if and only if the relative risk aversion of the representative investor is decreasing in terminal wealth.

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