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Skiba points in free end-time problems

Author

Listed:
  • Caulkins, Jonathan P.
  • Feichtinger, Gustav
  • Grass, Dieter
  • Hartl, Richard F.
  • Kort, Peter M.
  • Seidl, Andrea

Abstract

Since the end of the seventies Skiba points have been studied in infinite time optimal control problems with multiple steady states. At such a Skiba point the decision maker is indifferent between choosing trajectories that approach different steady states. This paper extends this theory towards free end-time optimal control problems, where the decision maker collects a salvage value at the endogenous horizon date. In particular, besides operating forever, the decision maker can choose to stop operations immediately, or to operate during a finite time interval after which the decision maker stops and collects a salvage value.

Suggested Citation

  • Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2015. "Skiba points in free end-time problems," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 404-419.
    • Handle: RePEc:eee:dyncon:v:51:y:2015:i:c:p:404-419
    DOI: 10.1016/j.jedc.2014.11.003
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    References listed on IDEAS

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    7. Jonathan Caulkins & Gustav Feichtinger & Richard Hartl & Peter Kort & Andreas Novak & Andrea Seidl, 2013. "Multiple equilibria and indifference-threshold points in a rational addiction model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 507-522, September.
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    Citations

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    Cited by:

    1. Francesco Bartaloni, 2021. "Existence of the Optimum in Shallow Lake Type Models with Hysteresis Effect," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 358-392, August.
    2. Seidl, Andrea & Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2018. "Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs," European Journal of Operational Research, Elsevier, vol. 267(2), pages 700-715.
    3. Feichtinger, Gustav & Grass, Dieter & Kort, Peter M. & Seidl, Andrea, 2021. "On the Matthew effect in research careers," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    4. Herbert Dawid & Michel Y. Keoula & Peter M. Kort, 2017. "Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms," Dynamic Games and Applications, Springer, vol. 7(4), pages 555-577, December.
    5. Feichtinger, G. & Grass, D. & Kort, P.M., 2019. "Optimal scientific production over the life cycle," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    6. Caulkins, Jonathan P. & Grass, Dieter & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Prskawetz, Alexia & Seidl, Andrea & Wrzaczek, Stefan, 2021. "The optimal lockdown intensity for COVID-19," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    7. Seidl, Andrea, 2019. "Zeno points in optimal control models with endogenous regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 353-368.
    8. Andrea Seidl & Stefan Wrzaczek & Fouad El Ouardighi & Gustav Feichtinger, 2016. "Optimal Career Strategies and Brain Drain in Academia," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 268-295, January.
    9. Gezer, Serhat, 2019. "Delaying product introduction: A dynamic analysis with endogenous time horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 96-114.
    10. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.

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    More about this item

    Keywords

    Optimal control; Skiba point; Capital accumulation model; Free end-time problem; Takeover;
    All these keywords.

    JEL classification:

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

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