Asset Pricing in a Production Economy with Heterogeneous Investors

Abstract

This paper is a theoretical examination of the stochastic behavior of equilibrium asset prices in an economy consisting of a production process controlled by a state variable representing the state of technology. The investors with different degrees of risk aversion and time preferences trade and lend among themselves in order to maximize their individual utilities of life time consumption. The allocation of wealth fluctuates randomly among them and acts as a state variable against which each investor wants to hedge. This hedging motive complicates the investor's portfolio choice and the equilibrium in the production economy. A general method of constructing equilibrium asset prices is developed and the wealth effect in the general equilibrium is discussed. The equilibrium market prices of risks and risk-free rate in a production economy with one representative investor has been presented by Cox, Ingersoll and Ross (1985). Considerable progress has been made by Dumas (1989) and Vasicek (2005) on the case of heterogeneous investors, however a complete description of the general equilibrium in the production economy with heterogeneous investors is yet to be developed. That is the focus of this paper. This paper establishes an economic model for the equilibrium asset prices by solving the joint optimization problem with proper market clearing conditions. The equilibrium conditions of the two party dynamic game are written as a set of two highly entangled nonlinear partial differential equations. The result can be extended to handle the case of multiple heterogeneous investors.