Asset Prices with Heterogeneity in Preferences and Beliefs

In this paper, we study asset prices in a dynamic, continuous-time, and general-equilibrium endowment economy in which agents have "catching up with the Joneses" utility functions and differ with respect to their beliefs (because of differences in priors) and their preference parameters for time discount, risk aversion, and sensitivity to habit. A key contribution of our paper is to demonstrate how one can obtain a closed-form solution to the consumption-sharing rule for agents who have both heterogeneous priors and heterogeneous preferences without restricting the risk aversion of the two agents to special values. We solve in closed form also for the state-price density, the risk-free interest rate and market price of risk, the stock price, equity risk premium, and volatility of stock returns, the term structure of interest rates, and the conditions necessary to obtain a stationary equilibrium in which both agents survive in the long run. The methodology we develop is sufficiently general in that, as long as markets are complete, it can be used to obtain the sharing rule and state prices for models set in discrete or continuous time and for arbitrary endowment and belief updating processes.