Heterogeneous Agent Models in Continuous Time. Achdou, Y., Lasry, J.M, Lions, P., & Moll, B. 2013.
Heterogeneous Agent Models in Continuous Time [pdf]Paper  abstract   bibtex   
In continuous time, a wide class of heterogeneous agent mode ls can be conveniently solved as systems of partial differential equations. This pap er develops tools for the analysis and numerical solution of such systems. We illustr ate our approach by study- ing a general equilibrium model with incomplete markets and uninsured idiosyncratic labor income risk as in Aiyagari (1994), Bewley (1986) and Hu ggett (1993). We de- velop an efficient algorithm for computing both stationary an d time-varying equilibria, and obtain three theoretical results: a tight characteriza tion of the speed at which households hit the borrowing constraint, an intuitive char acterization of the equilib- rium interest rate in terms of the number of borrowing constr aint households, and a proof of existence of a stationary equilibrium.

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