Fast Upper-Envelope Scan for Discrete-Continuous Dynamic Programming

Abstract

We introduce a fast upper-envelope scan (FUES) method to compute solutions for dynamic programming problems with continuous and discrete choices. The FUES method builds on the standard endogenous grid method (EGM). Standard EGM applied to problems with continuous and discrete choices does not by itself generate the optimal solution since the first order conditions used to generate the endogenous grid are necessary but not sufficient. FUES sequentially checks EGM candidate solution points and eliminates points not on the upper-envelope of the value correspondence by only allowing discontinuities in the policy function at non-concave sections of the value correspondence. FUES is computationally efficient, involves minimal coding time or analysis on the researcher side and does not require monotonicity assumptions on the problem. We also show that if the EGM grid size is sufficiently large, FUES is guaranteed to recover the optimal solution without error. FUES can be applied to many standard economic models, involving housing frictions, firm investment frictions, portfolio allocation or labor market participation decisions.

Keywords: dynamic programming, computational methods, non-convex optimization, Euler equations

JEL Classification: C63