Limit of the solutions for the finite horizon problems as the optimal solution to the infinite horizon optimization problems |
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| Authors: | Dapeng Cai Takashi Gyoshin Nitta |
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| Institution: | 1. Institute for Advanced Research, Nagoya University , Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan cai@iar.nagoya-u.ac.jp;3. Department of Mathematics, Faculty of Education , Mie University , Kurimamachiya 1577, Tsu, 514-8507, Japan |
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| Abstract: | In this paper, we consider how to construct the optimal solutions for the undiscounted discrete time infinite horizon optimization problems. We present the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problem under two modified overtaking criteria, as well as the conditions under which it is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of a simple one-sector growth model to examine the impacts of discounting on the optimal path. |
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| Keywords: | infinite horizon optimization discounting boundary condition overtaking criterion |
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