Universität Bonn

Department of Economics

MEF Seminar Wintersemester 2021/22

Jesse Perla (UBC) 15.12.2021

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. We avoid the curse of dimensionality thanks to three complementary techniques: (1) exploiting symmetry in the approximate law of motion and the value function; (2) constructing a concentration of measure to calculate high-dimensional expectations using a single Monte Carlo draw from the distribution of idiosyncratic shocks; and (3) designing and training deep learning architectures that exploit symmetry and concentration of measure. As an application, we find a global solution of a multi-firm version of the classic Lucas and Prescott (1971) model of investment under uncertainty. First, we compare the solution against a linear-quadratic Gaussian version for validation and benchmarking. Next, we solve the nonlinear version where no accurate or closed-form solution exists.
Wednesday, 15.12.21 - 03:00 PM - 04:30 PM
"Exploiting Symmetry in High-Dimensional Dynamic Programming"
via Zoom
Meeting ID: 975 1613 8512
not required
Institute for Macroeconomics and Econometrics
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