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A simple proof of the necessity of the transversality condition

Author

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  • Takashi Kamihigashi

    () (RIEB, Kobe University, Rokkodai, Nada, Kobe 657-8501, 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, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 427-433.
  • Handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:427-433 Note: Received: January 22, 2001; revised version: April 2, 2001
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    References listed on IDEAS

    as
    1. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    2. 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.
    3. Bezalel Peleg & Harl E. Ryder, 1972. "On Optimal Consumption Plans in a Multi-sector Economy," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 159-169.
    4. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Takashi Kamihigashi, 2016. "A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies with Strictly Monotone Preferences," Discussion Paper Series DP2016-32, Research Institute for Economics & Business Administration, Kobe University, revised Dec 2017.
    2. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2014. "Intertemporal equilibrium with production: bubbles and efficiency," Documents de travail du Centre d'Economie de la Sorbonne 14043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. repec:hal:journl:halshs-01223969 is not listed on IDEAS
    4. Hiraguchi, Ryoji, 2008. "Some foundations for multiplicative habits models," Journal of Macroeconomics, Elsevier, pages 873-884.
    5. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    6. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2015. "Intertemporal equilibrium with heterogeneous agents, endogenous dividends and collateral constraints," Documents de travail du Centre d'Economie de la Sorbonne 15067r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.
    7. Takuma Kunieda & Tarishi Matsuoka & Akihisa Shibata, 2017. "Asset Bubbles, Technology Choice, and Financial Crises," Discussion Paper Series 157, School of Economics, Kwansei Gakuin University, revised Feb 2017.
    8. Kamihigashi, Takashi, 2005. "Necessity of the transversality condition for stochastic models with bounded or CRRA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1313-1329, August.
    9. Bosi, Stefano & Le Van, Cuong & Pham, Ngoc-Sang, 2017. "Asset bubbles and efficiency in a generalized two-sector model," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 37-48.
    10. Cuong Le Van & Ngoc-Sang Pham, 2016. "Intertemporal equilibrium with financial asset and physical capital," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 155-199.
    11. Ravi Kashyap, 2016. "Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything," Papers 1604.04872, arXiv.org, revised May 2016.
    12. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2016. "Rational land and housing bubbles in infinite-horizon economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01314609, HAL.
    13. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2015-38, Research Institute for Economics & Business Administration, Kobe University.
    14. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
    15. Willem H. Buiter, 2003. "Helicopter Money: Irredeemable Fiat Money and the Liquidity Trap," NBER Working Papers 10163, National Bureau of Economic Research, Inc.
    16. Hiraguchi, Ryoji, 2011. "A two sector endogenous growth model with habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 430-441, April.
    17. Vasilev, Aleksandar, 2015. "The welfare effect of at income tax reform: the case of Bulgaria. Technical Appendix," EconStor Research Reports 124168, ZBW - German National Library of Economics.
    18. Dapeng Cai & Takashi Gyoshin Nitta, 2012. "Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems," Papers 1203.3869, arXiv.org.
    19. Takashi Kamihigashi, 2015. "A Simple No-Bubble Theorem for Deterministic Dynamic Economies," Discussion Paper Series DP2015-24, Research Institute for Economics & Business Administration, Kobe University.
    20. Stefano Bosi & Cuong Le Van & Ngoc-Sang Pham, 2015. "Intertemporal equilibrium with heterogeneous agents, endogenous dividends and borrowing constraints," Documents de travail du Centre d'Economie de la Sorbonne 15067, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    21. Takashi Kamihigashi, 2016. "A Simple Optimality-Based No-Bubble Theorem for Deterministic Sequential Economies," Discussion Paper Series DP2016-22, Research Institute for Economics & Business Administration, Kobe University.
    22. repec:hal:journl:halshs-01316876 is not listed on IDEAS
    23. repec:hal:journl:halshs-01314609 is not listed on IDEAS
    24. Pham, Ngoc-Sang, 2017. "Assets with possibly negative dividends," MPRA Paper 78193, University Library of Munich, Germany.

    More about this item

    Keywords

    Transversality condition; Reduced-form model; Dynamic optimization.;

    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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