Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models

In this paper, the authors develop a discretized version of the dynamic programming algorithm and study its convergence and stability properties. They show that the computed value function converges quadratically to the true value function and that the computed value function converges linearly, as the mesh size of the discretization converges to zero; further, the algorithm is stable. The authors also discuss several aspects of the implementation of their procedures as applied to some commonly studied growth models.