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A limited-feedback approximation scheme for optimal switching problems with execution delays

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  • Magnus Perninge

    (Linnaeus University)

Abstract

We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a probabilistic method. The main contribution is, however, a scheme for approximating the optimal control by limiting the information in the state-feedback. In a numerical example the approximation routine gives a considerable computational performance enhancement when compared to a conventional algorithm.

Suggested Citation

  • Magnus Perninge, 2018. "A limited-feedback approximation scheme for optimal switching problems with execution delays," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 347-382, June.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:3:d:10.1007_s00186-017-0620-2
    DOI: 10.1007/s00186-017-0620-2
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    References listed on IDEAS

    as
    1. Rene Carmona & Michael Ludkovski, 2008. "Pricing Asset Scheduling Flexibility using Optimal Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 405-447.
    2. Avner Bar-Ilan & Agnès Sulem, 1995. "Explicit Solution of Inventory Problems with Delivery Lags," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 709-720, August.
    3. Magnus Perninge & Lennart Söder, 2014. "Irreversible investments with delayed reaction: an application to generation re-dispatch in power system operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 195-224, April.
    4. Aïd, René & Federico, Salvatore & Pham, Huyên & Villeneuve, Bertrand, 2015. "Explicit investment rules with time-to-build and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 240-256.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    7. Bar-Ilan, Avner & Sulem, Agnes & Zanello, Alessandro, 2002. "Time-to-build and capacity choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 69-98, January.
    8. Aïd, René & Campi, Luciano & Langrené, Nicolas & Pham, Huyên, 2014. "A probabilistic numerical method for optimal multiple switching problems in high dimension," LSE Research Online Documents on Economics 63011, London School of Economics and Political Science, LSE Library.
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    10. Bruder, Benjamin & Pham, Huyên, 2009. "Impulse control problem on finite horizon with execution delay," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1436-1469, May.
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