An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information

Abstract

This paper provides sufficient conditions for the equilibrium price system and a vector of exogenously specified state variable processes to form a diffusion process in a pure exchange economy. The conditions involve smoothness of agents' utility functions and certain nice properties of the aggregate endowment process and the dividend processes of traded assets. In place of the dynamic programming, a martingale representation technique is utilized to characterize equilibrium portfolio policies. This technique is useful even when there does not exist a finite dimensional Markov structure in the economy and thus the Markovian stochastic dynamic programming is not applicable. A gents are shown to hold certain hedging mutual funds and the riskless asset. In contrast to earlier results, the market portfolio does not have a special role in hedging, since the markets are dynamically complete. When there exists a finite dimensional Markov system in the economy, the dimension of the hedging demand identified through the Markovian dynamic programming may be much larger than that identified by the martingale method. Copyright 1987 by The Econometric Society.