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Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems

Author

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  • Dapeng CAI

    (Institute for Advanced Research, Nagoya University, Nagoya, Japan)

  • Takashi Gyoshin NITTA

    (Department of Mathematics, Faculty of Education, Mie University, Tsu, Japan)

Abstract

We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under the overtaking criterion.

Suggested Citation

  • Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems," Papers 0803.4046, arXiv.org.
    • Handle: RePEc:arx:papers:0803.4046
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    References listed on IDEAS

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    1. Stern,Nicholas, 2007. "The Economics of Climate Change," Cambridge Books, Cambridge University Press, number 9780521700801.
    2. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 55-76, March.
    3. Heal, G., 1998. "Valuing the Future: Economic Theory and Sustainability," Papers 98-10, Columbia - Graduate School of Business.
    4. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-723, May.
    5. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(1), pages 1-18.
    6. Robert M. Solow, 1974. "The Economics of Resources or the Resources of Economics," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 12, pages 257-276, Palgrave Macmillan.
    7. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
    8. Cuong Le Van & Lisa Morhaim, 2006. "On optimal growth models when the discount factor is near 1 or equal to 1," Post-Print halshs-00096034, HAL.
    9. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 275-280.
    10. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    11. Hiroshi Atsumi, 1965. "Neoclassical Growth and the Efficient Program of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 127-136.
    12. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems," Papers 0803.4050, arXiv.org.
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