IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/10103.html
   My bibliography  Save this paper

A viability theory approach to a two-stage optimal control problem

Author

Listed:
  • Krawczyk, Jacek B.
  • Serea, Oana-Silvia

Abstract

A two-stage control problem is one, in which model parameters (“technology”) might be changed at some time. An optimal solution to utility maximisation for this class of problems needs to thus contain information on the time, at which the change will take place (0, finite or never) as well as the optimal control strategies before and after the change. For the change, or switch, to occur the “new technology” value function needs to dominate the “old technology” value function, after the switch. We charaterise the value function using the fact that its hypograph is a viability kernel of an auxiliary problem and study when the graphs can intersect and hence whether the switch can occur. Using this characterisation we analyse a technology switching problem.

Suggested Citation

  • Krawczyk, Jacek B. & Serea, Oana-Silvia, 2007. "A viability theory approach to a two-stage optimal control problem," MPRA Paper 10103, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:10103
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/10103/1/MPRA_paper_10103.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Martinet, Vincent & Thebaud, Olivier & Doyen, Luc, 2007. "Defining viable recovery paths toward sustainable fisheries," Ecological Economics, Elsevier, vol. 64(2), pages 411-422, December.
    2. Martinet, V. & Doyen, L., 2007. "Sustainability of an economy with an exhaustible resource: A viable control approach," Resource and Energy Economics, Elsevier, vol. 29(1), pages 17-39, January.
    3. Dominique Pujal & Patrick Saint-Pierre, 2006. "Capture Basin Algorithm for Evaluating and Managing Complex Financial Instruments," Computing in Economics and Finance 2006 186, Society for Computational Economics.
    4. Jacek Krawczyk & Rishab Sethi, 2007. "Satisficing Solutions for New Zealand Monetary Policy," Reserve Bank of New Zealand Discussion Paper Series DP2007/03, Reserve Bank of New Zealand.
    5. Bene, C. & Doyen, L. & Gabay, D., 2001. "A viability analysis for a bio-economic model," Ecological Economics, Elsevier, vol. 36(3), pages 385-396, March.
    6. 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.
    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. Krawczyk, Jacek B & Townsend, Wilbur, 2015. "Viability of an economy with constrained inequality," Working Paper Series 4689, Victoria University of Wellington, School of Economics and Finance.
    2. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 18839, Victoria University of Wellington, School of Economics and Finance.
    3. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 3432, Victoria University of Wellington, School of Economics and Finance.

    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. Krawczyk, Jacek B & Pharo, Alastair & Simpson, Mark, 2011. "Approximations to viability kernels for sustainable macroeconomic policies," Working Paper Series 1531, Victoria University of Wellington, School of Economics and Finance.
    2. Jacek B. Krawczyk & Vladimir P. Petkov, 2022. "A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent," Games, MDPI, vol. 13(5), pages 1-24, August.
    3. Krawczyk, Jacek B & Townsend, Wilbur, 2015. "Viability of an economy with constrained inequality," Working Paper Series 19335, Victoria University of Wellington, School of Economics and Finance.
    4. Krawczyk, Jacek B & Townsend, Wilbur, 2015. "Viability of an economy with constrained inequality," Working Paper Series 4689, Victoria University of Wellington, School of Economics and Finance.
    5. Jacek Krawczyk & Alastair Pharo & Oana Serea & Stewart Sinclair, 2013. "Computation of viability kernels: a case study of by-catch fisheries," Computational Management Science, Springer, vol. 10(4), pages 365-396, December.
    6. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 3432, Victoria University of Wellington, School of Economics and Finance.
    7. Krawczyk, Jacek B & Pharo, Alastair S, 2011. "Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems," Working Paper Series 1878, Victoria University of Wellington, School of Economics and Finance.
    8. Krawczyk, Jacek B. & Judd, Kenneth L., 2014. "Which economic states are sustainable under a slightly constrained tax-rate adjustment policy," MPRA Paper 59027, University Library of Munich, Germany.
    9. Baumgärtner, Stefan & Quaas, Martin F., 2009. "Ecological-economic viability as a criterion of strong sustainability under uncertainty," Ecological Economics, Elsevier, vol. 68(7), pages 2008-2020, May.
    10. Martinet, Vincent & Blanchard, Fabian, 2009. "Fishery externalities and biodiversity: Trade-offs between the viability of shrimp trawling and the conservation of Frigatebirds in French Guiana," Ecological Economics, Elsevier, vol. 68(12), pages 2960-2968, October.
    11. Doyen, L. & Thébaud, O. & Béné, C. & Martinet, V. & Gourguet, S. & Bertignac, M. & Fifas, S. & Blanchard, F., 2012. "A stochastic viability approach to ecosystem-based fisheries management," Ecological Economics, Elsevier, vol. 75(C), pages 32-42.
    12. Péreau, J.-C. & Doyen, L. & Little, L.R. & Thébaud, O., 2012. "The triple bottom line: Meeting ecological, economic and social goals with individual transferable quotas," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 419-434.
    13. Jacek Krawczyk & Rishab Sethi, 2007. "Satisficing Solutions for New Zealand Monetary Policy," Reserve Bank of New Zealand Discussion Paper Series DP2007/03, Reserve Bank of New Zealand.
    14. Krawczyk, Jacek B & Pharo, Alastair & Simpson, Mark, 2011. "Approximations to viability kernels for sustainable macroeconomic policies," Working Paper Series 18551, Victoria University of Wellington, School of Economics and Finance.
    15. Wei, W. & Alvarez, I. & Martin, S., 2013. "Sustainability analysis: Viability concepts to consider transient and asymptotical dynamics in socio-ecological tourism-based systems," Ecological Modelling, Elsevier, vol. 251(C), pages 103-113.
    16. Doyen, Luc & Péreau, Jean-Christophe, 2012. "Sustainable coalitions in the commons," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 57-64.
    17. Groot, Jeroen C.J. & Rossing, Walter a.H. & Tichit, Muriel & Turpin, Nadine & Jellema, André & Baudry, Jacques & Verburg, Peter & Doyen, Luc & van de Ven, Gerrie, 2009. "On the contribution of modelling to multifunctional agriculture: learning from comparisons," MPRA Paper 65467, University Library of Munich, Germany.
    18. Marc Leandri & Mabel Tidball, 2017. "Assessing the sustainability of optimal pollution paths in a world with inertia," Working Papers 2017.10, FAERE - French Association of Environmental and Resource Economists.
    19. A.A. Cisse & L. Doyen & F. Blanchard & J.C. Pereau, 2013. "Stochastic viability of the coastal fishery in French Guiana," Documents de Travail 2013-07, CEREGMIA, Université des Antilles et de la Guyane.
    20. Vincent Martinet & Michel de Lara & Julio Peña & Héctor Ramirez, 2010. "Evaluation of Management Procedures: Application to Chilean Jack Mackerel Fishery," ILADES-UAH Working Papers inv255, Universidad Alberto Hurtado/School of Economics and Business.

    More about this item

    Keywords

    value function; viability kernel; viscosity solutions;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    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:pra:mprapa:10103. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.