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Zeno points in optimal control models with endogenous regime switching

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  • Seidl, Andrea

Abstract

The present paper considers a type of multi-stage problem where a decision maker can optimally decide to switch between two alternating stages (regimes). In such a problem, either one of the two stages dominates in the long run or it is optimal to infinitely switch between stages. A point where such a phenomenon occurs with optimal switching time zero is called Zeno point.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:100:y:2019:i:c:p:353-368
    DOI: 10.1016/j.jedc.2018.09.010
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    References listed on IDEAS

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    1. Boucekkine, R. & Pommeret, A. & Prieur, F., 2013. "Optimal regime switching and threshold effects," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2979-2997.
    2. Boucekkine, Raouf & Saglam, Cagri & Valléee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 250-271, April.
    3. Long, Ngo Van & Prieur, Fabien & Tidball, Mabel & Puzon, Klarizze, 2017. "Piecewise closed-loop equilibria in differential games with regime switching strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 264-284.
    4. Tomiyama, Ken & Rossana, Robert J., 1989. "Two-stage optimal control problems with an explicit switch point dependence : Optimality criteria and an example of delivery lags and investment," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 319-337, July.
    5. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.
    6. 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.
    7. 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.
    8. 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.
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    10. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2013. "When to make proprietary software open source," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1182-1194.
    11. Tomiyama, Ken, 1985. "Two-stage optimal control problems and optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 9(3), pages 317-337, November.
    12. Elke Moser & Andrea Seidl & Gustav Feichtinger, 2014. "History-dependence in production-pollution-trade-off models: a multi-stage approach," Annals of Operations Research, Springer, vol. 222(1), pages 457-481, November.
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    14. Dieter Grass & Richard F. Hartl & Peter M. Kort, 2012. "Capital Accumulation and Embodied Technological Progress," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 588-614, August.
    15. Makris, Miltiadis, 2001. "Necessary conditions for infinite-horizon discounted two-stage optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1935-1950, December.
    16. Kort, Peter M. & Wrzaczek, Stefan, 2015. "Optimal firm growth under the threat of entry," European Journal of Operational Research, Elsevier, vol. 246(1), pages 281-292.
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    Cited by:

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    2. Hao, Shiming, 2021. "True structure change, spurious treatment effect? A novel approach to disentangle treatment effects from structure changes," MPRA Paper 108679, University Library of Munich, Germany.

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    More about this item

    Keywords

    Multi-stage modeling; Zeno point; Endogenous regime switching;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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