Dynamic programming is the foundation of dynamic economic analysis and often requires numerical solution methods. Standard methods are either slow or unstable. These instabilities are avoided when one uses modern methods from numerical optimization and approximation. Furthermore, large dynamic...

Efficient, accurate, multi-dimensional, numerical integration has become an important tool for approximating the integrals which arise in modern economic models built on unobserved heterogeneity, incomplete information, and uncertainty. This paper demonstrates that polynomialbased rules...