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...

We introduce a computational technique- precomputation of integrals - that makes it possible to construct conditional expectation functions in dynamic stochastic models in the initial stage of a solution procedure. This technique is very general: it works for a broad class of approximating...

Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games equilibria can be described as solutions of polynomial equations. In this paper we describe state-of-the-art techniques for...

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions. This paper uses Hermite data obtained from the optimization step and applies Hermite interpolation to construct approximate value functions. Several examples show that Hermite interpolation...

Continuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a...

We propose a novel methodology for evaluating the accuracy of numerical solutions to dynamic economic models. Specifically, we construct a lower bound on the size of approximation errors. A small lower bound on errors is a necessary condition for accuracy: If a lower error bound is unacceptably...

First, we propose a more efficient implementation of the Smolyak method for interpolation, namely, we show how to avoid costly evaluations of repeated basis functions in the conventional Smolyak formula. Second, we extend the Smolyak method to include anisotropic constructions; this allows us to...

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation methods, we examine a variety of alternatives, including least- squares methods using singular value decomposition and Tikhonov...

Discrete-time stochastic games with a finite number of states have been widely applied to study the strategic interactions among forward-looking players in dynamic environments. These games suffer from a “curse of dimensionality” when the cost of computing players’ expectations over all...

Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games, equilibria can be described as solutions of polynomial equations. In this paper, we describe state-of-the-art techniques for...