Equilibrium Existence and Approximation for Incomplete Market Models with Substantial Heterogeneity

41 Pages Posted: 24 Apr 2013

See all articles by Thomas M. Mertens

Thomas M. Mertens

Federal Reserve Bank of San Francisco

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace; Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP); National Bureau of Economic Research (NBER)

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Date Written: November 2012

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.

Keywords: Uninsurable risk, portfolio choice, perturbation methods

Suggested Citation

Mertens, Thomas M. and Judd, Kenneth L., Equilibrium Existence and Approximation for Incomplete Market Models with Substantial Heterogeneity (November 2012). NYU Working Paper No. 2451/31656. Available at SSRN: https://ssrn.com/abstract=2255879

Thomas M. Mertens (Contact Author)

Federal Reserve Bank of San Francisco ( email )

101 Market Street
San Francisco, CA 94105
United States

Kenneth L. Judd

Stanford University - The Hoover Institution on War, Revolution and Peace ( email )

Stanford, CA 94305-6010
United States

Center for Robust Decisionmaking on Climate & Energy Policy (RDCEP) ( email )

5735 S. Ellis Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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