The Dynamics of Heterogeneity and Asset Prices

Abstract

In the context of a continuous-time pure-exchange economy model, the paper develops a novel methodology, based on measure-valued stochastic processes, for analyzing the evolution of heterogeneity in a tractable manner and studying its impact on asset prices. The agents in the economy differ with respect to impatience, risk aversion, beliefs about the growth rate of output, and to the rules for updating beliefs. The heterogeneity itself is described by a single object, a measure, and its dynamics by a measure-valued stochastic process. A key contribution of the paper consists in obtaining a closed form formula for the stock price in the case in which preferences are homogeneous with the risk aversion parameter given by a natural number. We also synthesize and generalize existing results about the equilibrium in heterogeneous pure-exchange complete markets economies and we highlight the importance of the endogenously determined risk tolerance weighted consumption distribution as a key ingredient in driving the equilibrium variables.