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Monotone optimal trajectories

Author

Listed:
  • Niko Jaakkola

    (University of Bologna)

  • Florian Wagener

    (University of Amsterdam)

Abstract

We give weak conditions for a continuous time optimal control problem with one-dimensional state space to have monotone optimal trajectories. These conditions include a concavity condition on the Lagrange function. If that condition is changed to strict concavity, then all optimal trajectories are monotone.

Suggested Citation

  • Niko Jaakkola & Florian Wagener, 2025. "Monotone optimal trajectories," Tinbergen Institute Discussion Papers 25-061/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20250061
    as

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    References listed on IDEAS

    as
    1. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    2. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
    3. Hartl, Richard F., 1987. "A simple proof of the monotonicity of the state trajectories in autonomous control problems," Journal of Economic Theory, Elsevier, vol. 41(1), pages 211-215, February.
    4. Akao, Ken-Ichi & Kamihigashi, Takashi & Nishimura, Kazuo, 2025. "Critical capital stock in a continuous-time growth model with a convex-concave production function," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    5. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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