Nerlove–Arrow: A New Solution to an Old Problem

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• 作者：Marc Artzrouni ; Patrice Cassagnard
• 关键词：Nerlove–Arrow ; Dynamic programming ; Optimization ; Turnpike
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：172
• 期：1
• 页码：267-280
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

We use the optimality principle of dynamic programming to formulate a discrete version of the original Nerlove–Arrow maximization problem. When the payoff function is concave, we give a simple recursive process that yields an explicit solution to the problem. If the time horizon is long enough, there is a “transiently stationary” (turnpike) value for the optimal capital after which the capital must be left to depreciate as it takes the exit ramp. If the time horizon is short, the capital is left to depreciate. Simple closed-form solutions are given for a power payoff function.