Optimal time aggregation of infinite horizon control problems

Abstract

This paper proposes a novel method that enhances numerical approximation of infinite horizon optimal control problems. For direct numerical optimization, a continuous-time infinite horizon model needs to be first recast as a discrete-time, finite-horizon control problem. The very transformation itself may significantly degrade the quality of the optimization results, if due care is not taken to preserve the salient features in the original model. Michel (1994. Econometrica 62, 635-656, 2001. Journal of Economic Dynamics and Control 25, 1179-1191), for instance, propose time aggregation methods that minimize approximation errors at the steady-state. Using their scheme, we show that overall optimization performance can be further improved if the discretization of the transient phase is optimal as well. Three sample problems are numerically solved to demonstrate the potential benefits. r 2005 Elsevier B.V. All rights reserved.JEL classification: C61; C63

Multidimensional Transitional Dynamics: A Simple Numerical Procedure

“…Applying the necessary and sufficient conditions stated by Michel (1994, 2001) yields a considerable improvement in the numerical accuracy of the discrete-time model. Moreover, Alemdar et al (2006) show that the overall optimization performance can be improved substantially if an optimal allocation of the time mesh is chosen for the transition. Our approach is to solve the system of differential equations directly.…”

Steady-state invariance in high-order Runge–Kutta discretization of optimal growth models

“…Indeed, our schemes satisfy both conditions (19) and (20), without requiring any restriction on the time step-length D n . This allows us to use either exponential temporal grids similar to those in Mercenier and Michel (2001) or temporal stepsizes as added control variables like in Alemdar et al (2006).…”