Open AccessA nonlinear certainty equivalent approximation method for dynamic stochastic problems
Author(s) -
Cai Yongyang,
Judd Kenneth,
Steinbuks Jevgenijs
Publication year - 2017
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe533
Subject(s) - nonlinear system , certainty , mathematical optimization , linearization , mathematics , linear approximation , computer science , physics , geometry , quantum mechanics
This paper introduces a nonlinear certainty‐equivalent approximation method for dynamic stochastic problems. We first introduce a novel, stable, and efficient method for computing the decision rules in deterministic dynamic economic problems. We use the results as nonlinear and global certainty‐equivalent approximations for solutions to stochastic problems, and compare their accuracy to the common linear and local certainty‐equivalent methods. Our examples demonstrate that this method can be applied to solve high‐dimensional problems with up to 400 state variables with acceptable accuracy. This method can also be applied to solve problems with inequality constraints. These features make the nonlinear certainty‐equivalent approximation method suitable for solving complex economic problems, where other algorithms, such as log‐linearization, fail to produce a valid global approximation or are far less tractable.