A nonlinear certainty equivalent approximation method for dynamic stochastic problems

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 approx- imations for solutions to stochastic problems, and compare their accuracy to the common linear and local certainty-equivalent methods. Our examples demon- strate 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 non- linear 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.