On the optimal control of a linear neutral differential equation arising in economics

In this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, and the second follows a dynamic programming approach. Because of the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting HamiltonJacobiBellman equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared with the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs. Copyright (c) 2011 John Wiley & Sons, Ltd.