IDEAS home Printed from https://ideas.repec.org/p/zbw/tuweco/062019.html
   My bibliography  Save this paper

Using age-structure for a multi-stage optimal control model with random switching time

Author

Listed:
  • Wrzaczek, Stefan
  • Kuhn, Michael
  • Frankovic, Ivan

Abstract

The paper presents a transformation of a multi-stage optimal control model with random switching time to an age-structured optimal control model. Following the mathematical transformation, the advantages of the present approach, as compared to a standard backward approach, are discussed. They relate in particular to a compact and unified representation of the two stages of the model, the applicability of well-known numerical solution methods, and the illustration of state- and control dynamics. The paper closes with a simple example on a macroeconomic shock, illustrating the workings and advantages of the approach.

Suggested Citation

  • Wrzaczek, Stefan & Kuhn, Michael & Frankovic, Ivan, 2019. "Using age-structure for a multi-stage optimal control model with random switching time," ECON WPS - Working Papers in Economic Theory and Policy 06/2019, TU Wien, Institute of Statistics and Mathematical Methods in Economics, Economics Research Unit.
    • Handle: RePEc:zbw:tuweco:062019
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/204558/1/1677968591.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    4. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 1998. "Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-384, December.
    5. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, September.
    6. Raouf Boucekkine & David de la Croix & Omar Licandro, 2006. "Vintage Capital," Economics Working Papers ECO2006/8, European University Institute.
    7. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2015. "Optimal choice of health and retirement in a life-cycle model," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 186-212.
    8. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    9. Robert J. Barro, 2015. "Environmental Protection, Rare Disasters and Discount Rates," Economica, London School of Economics and Political Science, vol. 82(325), pages 1-23, January.
    10. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2011. "Externalities in a life cycle model with endogenous survival," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 627-641.
    11. Frederick Ploeg & Aart Zeeuw, 2019. "Pricing Carbon and Adjusting Capital to Fend Off Climate Catastrophes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 29-50, January.
    12. Wrzaczek, Stefan & Kuhn, Michael & Prskawetz, Alexia & Feichtinger, Gustav, 2010. "The reproductive value in distributed optimal control models," Theoretical Population Biology, Elsevier, vol. 77(3), pages 164-170.
    13. Ian W. R. Martin & Robert S. Pindyck, 2015. "Averting Catastrophes: The Strange Economics of Scylla and Charybdis," American Economic Review, American Economic Association, vol. 105(10), pages 2947-2985, October.
    14. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.
    15. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    16. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    17. Boucekkine, Raouf & del Rio, Fernando & Licandro, Omar, 1999. "Endogenous vs Exogenously Driven Fluctuations in Vintage Capital Models," Journal of Economic Theory, Elsevier, vol. 88(1), pages 161-187, September.
    18. Alain Bensoussan & Suresh P. Sethi, 2007. "The Machine Maintenance and Sale Age Model of Kamien and Schwartz Revisited," Management Science, INFORMS, vol. 53(12), pages 1964-1976, December.
    19. 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.
    20. Martin L. Weitzman, 2014. "Fat Tails and the Social Cost of Carbon," American Economic Review, American Economic Association, vol. 104(5), pages 544-546, May.
    21. Michael R. Caputo & Martin Forster, 2016. "Optimal plans and timing under additive transformations to rewards," Oxford Economic Papers, Oxford University Press, vol. 68(2), pages 604-626.
    22. Frederick van der Ploeg & Aart de Zeeuw, 2018. "Climate Tipping and Economic Growth: Precautionary Capital and the Price of Carbon," Journal of the European Economic Association, European Economic Association, vol. 16(5), pages 1577-1617.
    23. Vallée, Thomas & Moreno-Galbis, Eva, 2011. "Optimal time switching from tayloristic to holistic workplace organization," Structural Change and Economic Dynamics, Elsevier, vol. 22(3), pages 238-246, September.
    24. Robert J. Barro & José F. Ursúa, 2012. "Rare Macroeconomic Disasters," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 83-109, July.
    25. Kuhn, Michael & Wrzaczek, Stefan & Oeppen, Jim, 2010. "Recognizing progeny in the value of life," Economics Letters, Elsevier, vol. 107(1), pages 17-21, April.
    26. John Laitner & Dan Silverman & Dmitriy Stolyarov, 2018. "The Role of Annuitized Wealth in Post-retirement Behavior," American Economic Journal: Macroeconomics, American Economic Association, vol. 10(3), pages 71-117, July.
    27. Morton I. Kamien & Nancy L. Schwartz, 1971. "Optimal Maintenance and Sale Age for a Machine Subject to Failure," Management Science, INFORMS, vol. 17(8), pages 495-504, April.
    28. B. Skritek & V. M. Veliov, 2015. "On the Infinite-Horizon Optimal Control of Age-Structured Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 243-271, October.
    29. 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.
    30. Audrey Laporte & Brian Ferguson, 2007. "Investment in health when health is stochastic," Journal of Population Economics, Springer;European Society for Population Economics, vol. 20(2), pages 423-444, April.
    31. 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.
    32. 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.
    33. John B. Burbidge & A. Leslie Robb, 1980. "Pensions and Retirement Behaviour," Canadian Journal of Economics, Canadian Economics Association, vol. 13(3), pages 421-437, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.

    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. Kuhn, Michael & Wrzaczek, Stefan & Prskawetz, Alexia & Feichtinger, Gustav, 2015. "Optimal choice of health and retirement in a life-cycle model," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 186-212.
    2. 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.
    3. 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.
    4. 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.
    5. Kuhn, Michael & Frankovic, Ivan & Wrzaczek, Stefan, 2017. "Medical Progress, Demand for Health Care, and Economic Performance," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168249, Verein für Socialpolitik / German Economic Association.
    6. Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2020. "Optimal switching from competition to cooperation: a preliminary exploration," Working Papers halshs-02434786, HAL.
    7. Raouf Boucekkine & David Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
    8. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona School of Economics.
    9. Behringer, Stefan & Upmann, Thorsten, 2017. "Harvesting a Remote Renewable Resource," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168250, Verein für Socialpolitik / German Economic Association.
    10. Frankovic, Ivan & Kuhn, Michael & Wrzaczek, Stefan, 2016. "Medical care within an OLG economy with realistic demography," ECON WPS - Working Papers in Economic Theory and Policy 02/2016, TU Wien, Institute of Statistics and Mathematical Methods in Economics, Economics Research Unit.
    11. Camacho, Carmen & Hassan, Waleed, 2023. "The dynamics of revolution: Discrimination, social unrest and the optimal timing of revolution," Economic Modelling, Elsevier, vol. 128(C).
    12. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
    13. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2005. "Environmental policy, the porter hypothesis and the composition of capital: Effects of learning and technological progress," Journal of Environmental Economics and Management, Elsevier, vol. 50(2), pages 434-446, September.
    14. Wrzaczek, Stefan & Kuhn, Michael & Prskawetz, Alexia & Feichtinger, Gustav, 2010. "The reproductive value in distributed optimal control models," Theoretical Population Biology, Elsevier, vol. 77(3), pages 164-170.
    15. Ngo Van Long & Fabien Prieur & Klarizze Puzon & Mabel Tidball, 2013. "Markov Perfect Equilibria in Differential Games with Regime Switching Strategies," Working Papers 13-06, LAMETA, Universtiy of Montpellier, revised Jan 2014.
    16. Dogan, Erol & Le Van, Cuong & Saglam, Cagri, 2011. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 97-103, March.
    17. Caliendo, Frank N. & Gorry, Aspen & Slavov, Sita, 2019. "The cost of uncertainty about the timing of Social Security reform," European Economic Review, Elsevier, vol. 118(C), pages 101-125.
    18. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2008. "Financially constrained capital investments: The effects of disembodied and embodied technological progress," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 459-483, April.
    19. Augeraud-Veron, Emmanuelle & Bambi, Mauro, 2015. "Endogenous growth with addictive habits," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 15-25.
    20. Richard F. Hartl & Peter M. Kort & Andrea Seidl, 2020. "Decisions on pricing, capacity investment, and introduction timing of new product generations in a durable-good monopoly," 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. 28(2), pages 497-519, June.

    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:zbw:tuweco:062019. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/imtuwat.html .

    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.