Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems

Details Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems Treating the Future Equally: Solving Undiscounted Infinite Horizon Optimization Problems

2007-01-13

arxiv.org/abs/math/0701371v4

ROMAI J., 6, 2(2010), 199--220

Mathematics

Optimization and Control

40 pages

Scientific paper

Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we show that under two fairly general conditions, the limit of the solution to the undiscounted finite horizon problem is optimal among feasible paths for the undiscounted infinite horizon problem, in the sense of the overtaking criterion. Applied to a simple Ramsey model, we show that the derived path contains intriguing properties. We also comprehend the legitimacy of the derived paths by addressing the perplexities with non-standard arguments.

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