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Pricing Asset Scheduling Flexibility using Optimal Switching


  • Rene Carmona
  • Michael Ludkovski


We study the financial engineering aspects of operational flexibility of energy assets. The current practice relies on a representation that uses strips of European spark-spread options, ignoring the operational constraints. Instead, we propose a new approach based on a stochastic impulse control framework. The model reduces to a cascade of optimal stopping problems and directly demonstrates that the optimal dispatch policies can be described with the aid of 'switching boundaries', similar to the free boundaries of standard American options. Our main contribution is a new method of numerical solution relying on Monte Carlo regressions. The scheme uses dynamic programming to efficiently approximate the optimal dispatch policy along the simulated paths. Convergence analysis is carried out and results are illustrated with a variety of concrete computational examples. We benchmark and compare our scheme with alternative numerical methods.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:405-447
    DOI: 10.1080/13504860802170507

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    1. repec:eee:energy:v:144:y:2018:i:c:p:887-902 is not listed on IDEAS
    2. repec:eee:appene:v:204:y:2017:i:c:p:531-543 is not listed on IDEAS
    3. Randall Martyr, 2014. "Solving finite time horizon Dynkin games by optimal switching," Papers 1411.4438,, revised Jan 2016.
    4. 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.
    5. repec:dau:papers:123456789/11439 is not listed on IDEAS
    6. Woo, C.K. & Moore, J. & Schneiderman, B. & Ho, T. & Olson, A. & Alagappan, L. & Chawla, K. & Toyama, N. & Zarnikau, J., 2016. "Merit-order effects of renewable energy and price divergence in California’s day-ahead and real-time electricity markets," Energy Policy, Elsevier, vol. 92(C), pages 299-312.
    7. Chi-Keung Woo, Ira Horowitz, Jay Zarnikau, Jack Moore, Brendan Schneiderman, Tony Ho, and Eric Leung, 2016. "What Moves the Ex Post Variable Profit of Natural-Gas-Fired Generation in California?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    8. Lin Zhao & Sweder van Wijnbergen, 2015. "Asset Pricing in Incomplete Markets: Valuing Gas Storage Capacity," Tinbergen Institute Discussion Papers 15-104/VI/DSF95, Tinbergen Institute.
    9. Gassiat, Paul & Kharroubi, Idris & Pham, Huyên, 2012. "Time discretization and quantization methods for optimal multiple switching problem," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2019-2052.
    10. El Asri, Brahim, 2013. "Stochastic optimal multi-modes switching with a viscosity solution approach," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 579-602.
    11. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455,, revised Aug 2010.
    12. 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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