Solving General Incomplete Market Models with Substantial Heterogeneity

We propose a simple but general solution method for models with incomplete markets and finitely but arbitrarily many heterogeneous agents. Our method can handle many state and choice variables for each agent and thus an extremely high-dimensional state space. The solution technique is based on perturbation methods that build an approximation around a point at which the solution is known. At this point, agents are either identical or their policy functions are known. The novel idea is to exploit the symmetry of the problem to avoid the curse of dimensionality. Our method underlies an approximation theory that specifies the speed and radius of convergence as well as the class of models to which our method applies. As a result, we study the interaction between uninsurable idiosyncratic labor income risk and asset price dynamics within a standard macroeconomic model. We show that not only the variability of individual wealth but also its comovement with other agentsâ wealth plays an important role.