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On the optimal control of a linear neutral differential equation arising in economics. (English) Zbl 1311.49064
Summary: 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 Hamilton-Jacobi-Bellman 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.

MSC:
49L20 Dynamic programming in optimal control and differential games
49J15 Existence theories for optimal control problems involving ordinary differential equations
34K40 Neutral functional-differential equations
91B55 Economic dynamics
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