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 use a novel, stable and efficient method for computing the optimal policy functions for deterministic dynamic optimization problems, and then use them as certainty-equivalent approximations for the stochastic versions. Our examples demonstrate that it can be applied to solve high-dimensional problems with up to four hundred state variables with an acceptable accuracy. This method can also be applied to solve problems with inequality constraints that occasionally bind. These features make the nonlinear certainty equivalent approximation method suitable for solving complex economic problems, where other algorithms, such as log-linearization, fail or are far less tractable