Equilibrium Existence and Approximation for Incomplete Market Models with Substantial Heterogeneity

Abstract

This paper contains an analysis of incomplete market models with finitely but arbitrarily many heterogeneous agents. We discuss the mathematical foundation for equilibrium conditions which leads to two findings. First, we establish existence of equilibria for small and large risks. Second, we develop a simple but general solution technique which handles many state and choice variables for each agent and thus an extremely high-dimensional state space. The method is based on perturbations around a point at which the solution is known. The novel idea is to exploit the symmetry of the problem to overcome the curse of dimensionality. We use the analysis to demonstrate the impact of heterogeneity on macroeconomic quantities and the pricing of risk. Furthermore, we set our technique apart from the standard method used in the literature.