Optimal Discretization of Continuous-Time Control Problems

Nonlinear infinite horizon continuous time optimization problems are widely used in economics. However numerical solutions necessarily require reformulating the problem into a discrete finite approximation. The method proposed by Mercenier and Michel (1994) minimizes approximation error at steady state but leaves unanswered the question of minimizing approximation errors along the transient path. In this paper, we address that problem as well. That is, with steady state invariance we minimize error at steady state, but by optimally choosing time intervals along the transient path, we find optimal commitment periods which have many business and economics applications. In the paper, the method has been mathematically proved and numerically tested using genetic algorithms.