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

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/10103/1/MPRA_paper_10103.pdf
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    References listed on IDEAS

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    1. 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.
    2. Martinet, Vincent & Thebaud, Olivier & Doyen, Luc, 2007. "Defining viable recovery paths toward sustainable fisheries," Ecological Economics, Elsevier, vol. 64(2), pages 411-422, December.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    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 3432, Victoria University of Wellington, School of Economics and Finance.

    More about this item

    Keywords

    value function; viability kernel; viscosity solutions;

    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

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