IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v20y2002i2p427-433.html
   My bibliography  Save this article

A simple proof of the necessity of the transversality condition

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00199/papers/2020002/20200427.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ravi Kashyap, 2016. "Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything," Papers 1604.04872, arXiv.org, revised Sep 2019.
    2. Buiter, Willem H. & Sibert, Anne C., 2007. "Deflationary Bubbles," Macroeconomic Dynamics, Cambridge University Press, vol. 11(4), pages 431-454, September.
    3. 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.
    4. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    5. Mitra, Tapan & Roy, Santanu, 2017. "Optimality of Ramsey–Euler policy in the stochastic growth model," Journal of Economic Theory, Elsevier, vol. 172(C), pages 1-25.
    6. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University.
    7. Tapan Mitra & Santanu Roy, 2022. "Propensity to consume and the optimality of Ramsey–Euler policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 55-89, February.
    8. Takashi Kamihigashi, 2016. "A Generalization of Fatou's Lemma for Extended Real-Valued Functions on σ-Finite Measure Spaces: With an Application to Infinite-Horizon Optimization in Discrete Time," Discussion Paper Series DP2016-37, Research Institute for Economics & Business Administration, Kobe University, revised Jan 2017.
    9. 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.
    10. Dapeng Cai & Takashi Gyoshin Nitta, 2012. "Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems," Papers 1203.3869, arXiv.org.
    11. Takashi Kamihigashi, 2011. "Recurrent Bubbles," The Japanese Economic Review, Japanese Economic Association, vol. 62(1), pages 27-62, March.
    12. repec:dau:papers:123456789/3682 is not listed on IDEAS
    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, 2017. "Regime-Switching Sunspot Equilibria in a One-Sector Growth Model with Aggregate Decreasing Returns and Small Externalities," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 125-146, Springer.
    15. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
    16. Willem H. Buiter, 2003. "Helicopter Money: Irredeemable Fiat Money and the Liquidity Trap," NBER Working Papers 10163, National Bureau of Economic Research, Inc.
    17. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    18. 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.
    19. 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.
    20. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    21. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.

    More about this item

    Keywords

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:427-433. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.