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Energy contracts management by stochastic programming techniques


  • J. Bonnans


  • Zhihao Cen
  • Thibault Christel


We consider the problem of optimal management of energy contracts, with bounds on the local (time step) amounts and global (whole period) amounts to be traded, integer constraint on the decision variables and uncertainty on prices only. After building a finite state Markov chain by using vectorial quantization tree method, we rely on the stochastic dual dynamic programming (SDDP) method to solve the continuous relaxation of this stochastic optimization problem. An heuristic for computing sub optimal solutions to the integer optimization problem, based on the Bellman values of the continuous relaxation, is provided. Combining the previous techniques, we are able to deal with high-dimensional state variables problems. Numerical tests applied to realistic energy markets problems have been performed. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • J. Bonnans & Zhihao Cen & Thibault Christel, 2012. "Energy contracts management by stochastic programming techniques," Annals of Operations Research, Springer, vol. 200(1), pages 199-222, November.
  • Handle: RePEc:spr:annopr:v:200:y:2012:i:1:p:199-222:10.1007/s10479-011-0973-5
    DOI: 10.1007/s10479-011-0973-5

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    References listed on IDEAS

    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Bally, Vlad & Pagès, Gilles, 2003. "Error analysis of the optimal quantization algorithm for obstacle problems," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 1-40, July.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    5. repec:spr:compst:v:70:y:2009:i:1:p:13-33 is not listed on IDEAS
    6. Olivier Bardou & Sandrine Bouthemy & Gilles Pages, 2009. "Optimal Quantization for the Pricing of Swing Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(2), pages 183-217.
    7. Evgueni Gordienko & Enrique Lemus-Rodríguez & Raúl Montes-de-Oca, 2009. "Average cost Markov control processes: stability with respect to the Kantorovich metric," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 13-33, August.
    8. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    9. Guoming Lai & François Margot & Nicola Secomandi, 2010. "An Approximate Dynamic Programming Approach to Benchmark Practice-Based Heuristics for Natural Gas Storage Valuation," Operations Research, INFORMS, vol. 58(3), pages 564-582, June.
    10. 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.
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    Cited by:

    1. Giorgia Callegaro & Lucio Fiorin & Martino Grasselli, 2019. "Quantization meets Fourier: a new technology for pricing options," Annals of Operations Research, Springer, vol. 282(1), pages 59-86, November.
    2. Mahmutoğulları, Ali İrfan & Çavuş, Özlem & Aktürk, M. Selim, 2018. "Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR," European Journal of Operational Research, Elsevier, vol. 266(2), pages 595-608.
    3. Secomandi, Nicola & Seppi, Duane J., 2014. "Real Options and Merchant Operations of Energy and Other Commodities," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 6(3-4), pages 161-331, July.
    4. Bruno, Sergio & Ahmed, Shabbir & Shapiro, Alexander & Street, Alexandre, 2016. "Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 250(3), pages 979-989.
    5. Löhndorf, Nils & Shapiro, Alexander, 2019. "Modeling time-dependent randomness in stochastic dual dynamic programming," European Journal of Operational Research, Elsevier, vol. 273(2), pages 650-661.


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