Limit of the solutions for the finite horizon problems as the optimal solution to the infinite horizon optimization problems

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...

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Bibliographic Details
Published in:Journal of difference equations and applications 2011-03, Vol.17 (3), p.359-373
Main Authors: Cai, Dapeng, Nitta, Takashi Gyoshin
Format: Article
Language:English
Subjects:
boundary condition
Boundary conditions
Boundary value problems
Construction
Criteria
Difference equations
discounting
Horizon
infinite horizon optimization
Mathematical analysis
Mathematical functions
Mathematical models
Optimization
Overtaking
overtaking criterion
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Summary: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.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190902953763