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A Simple Proof of the Necessity of the Transversality Condition

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of the transversality condition can be shown in a straightforward way.

Suggested Citation

  • Takashi Kamihigashi, 2001. "A Simple Proof of the Necessity of the Transversality Condition," Discussion Paper Series 116, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:116
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp116.pdf
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    References listed on IDEAS

    as
    1. Araujo, A. & Scheinkman, J. A., 1983. "Maximum principle and transversality condition for concave infinite horizon economic models," Journal of Economic Theory, Elsevier, vol. 30(1), pages 1-16, June.
    2. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
    3. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    4. Takashi Kamihigashi, 2000. "A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 463-468.
    5. Bezalel Peleg & Harl E. Ryder, 1972. "On Optimal Consumption Plans in a Multi-sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 159-169.
    6. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    7. Ivar Ekeland & José Alexandre Scheinkman, 1986. "Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 216-229, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Programming; Dynamic Optimization; Models;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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