Using dynamic programming with adaptive grid scheme for optimal control problems in economics

An adaptive grid scheme that follows Grune is used to find the global solutions of discrete time Hamilton-Jacobi-Bellman equations, establishing local error estimates and developing an adapting iteration for the discretization of the grid space. The advantage of the use of the adaptive grid scheme is evident after computing the solutions of one- and two-dimensional economic models exhibiting steep curvature, complicated dynamics thresholds separating domains of attraction and periodic solutions. Deterministic and stochastic model variants are considered.