Asset price dynamics with heterogeneous, boundedly rational, utility-optimizing agents

P. M. Beaumont, A. J. Culham, Alec N. Kercheval

We examine market dynamics in a discrete-time, Lucas-style asset- pricing model with heterogeneous, utility-optimizing agents. Finitely many agents trade a single asset paying a stochastic dividend, and know the probability distribution of the dividend but not the private information of other agents. The market clearing price is determined endogenously in each period such that supply always equals demand. The resulting market price and agents' demands are functions of the dividend; equilibrium means these functions are at steady-state.

Our aim is to determine whether and how the pricing function evolves toward equilibrium. In case all agents have logarithmic utility, but possibly different holdings and discount factors, we completely describe the market dynamics, including the evolution of the pricing and demand functions, and asset holdings of the agents. The market converges to a stable equilibrium state where only the most patient agents remain, and the equilibrium pricing function is the same as the one arising in the simple homogeneous setting.