Fast Upper-Envelope Scan for Discrete-Continuous Dynamic Programming

27 Pages Posted: 12 Aug 2022 Last revised: 25 Oct 2022

See all articles by Loretti Dobrescu

Loretti Dobrescu

UNSW Australia Business School, School of Economics

Akshay Shanker

Australian National University (ANU) - Crawford School of Public Policy

Date Written: August 4, 2022

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

Suggested Citation

Dobrescu, Loretti Isabella and Shanker, Akshay, Fast Upper-Envelope Scan for Discrete-Continuous Dynamic Programming (August 4, 2022). UNSW Business School Research Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=4181302 or http://dx.doi.org/10.2139/ssrn.4181302

Loretti Isabella Dobrescu

UNSW Australia Business School, School of Economics ( email )

High Street
Sydney, NSW 2052
Australia

Akshay Shanker (Contact Author)

Australian National University (ANU) - Crawford School of Public Policy ( email )

ANU College of Asia and the Pacific
J.G. Crawford Building, #132, Lennox Crossing
Canberra, Australian Capital Territory 0200
Australia

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