IDEAS home Printed from https://ideas.repec.org/a/spr/eurjco/v8y2020i2d10.1007_s13675-020-00123-y.html
   My bibliography  Save this article

On conditional cuts for stochastic dual dynamic programming

Author

Listed:
  • W. Ackooij

    () (OSIRIS)

  • X. Warin

    () (OSIRIS)

Abstract

Multistage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management. A popular method is stochastic dual dynamic programming (SDDP), especially when the dimensionality of the problem is large and dynamic programming is no longer an option. The usual assumption of SDDP is that uncertainty is stage-wise independent, which is highly restrictive from a practical viewpoint. When possible, the usual remedy is to increase the state-space to account for some degree of dependency. In applications, this may not be possible or it may increase the state-space by too much. In this paper, we present an alternative based on keeping a functional dependency in the SDDP—cuts related to the conditional expectations in the dynamic programming equations. Our method is based on popular methodology in mathematical finance, where it has progressively replaced scenario trees due to superior numerical performance. We demonstrate the interest of combining this way of handling dependency in uncertainty and SDDP on a set of numerical examples. Our method is readily available in the open-source software package StOpt.

Suggested Citation

  • W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
  • Handle: RePEc:spr:eurjco:v:8:y:2020:i:2:d:10.1007_s13675-020-00123-y
    DOI: 10.1007/s13675-020-00123-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13675-020-00123-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Homem-de-Mello, Tito & Pagnoncelli, Bernardo K., 2016. "Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective," European Journal of Operational Research, Elsevier, vol. 249(1), pages 188-199.
    2. 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.
    3. repec:dau:papers:123456789/5524 is not listed on IDEAS
    4. Patrick Henaff & Ismail Laachir & Francesco Russo, 2013. "Gas storage valuation and hedging. A quantification of the model risk," Papers 1312.3789, arXiv.org.
    5. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
    6. Shapiro, Alexander & Tekaya, Wajdi & da Costa, Joari Paulo & Soares, Murilo Pereira, 2013. "Risk neutral and risk averse Stochastic Dual Dynamic Programming method," European Journal of Operational Research, Elsevier, vol. 224(2), pages 375-391.
    7. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    8. repec:dau:papers:123456789/4273 is not listed on IDEAS
    9. Vincent Guigues, 2014. "SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning," Computational Optimization and Applications, Springer, vol. 57(1), pages 167-203, January.
    10. Z. L. Chen & W. B. Powell, 1999. "Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 497-524, September.
    11. K. Linowsky & A. B. Philpott, 2005. "On the Convergence of Sampling-Based Decomposition Algorithms for Multistage Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 349-366, May.
    12. repec:dau:papers:123456789/11531 is not listed on IDEAS
    13. Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.
    14. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    15. Rene Carmona & Michael Ludkovski, 2010. "Valuation of energy storage: an optimal switching approach," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 359-374.
    16. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    17. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    18. Wim Ackooij & Welington Oliveira & Yongjia Song, 2019. "On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 1-42, September.
    19. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    20. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    21. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, February.
    22. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    23. 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.
    24. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    25. Guigues, Vincent & Sagastizábal, Claudia, 2012. "The value of rolling-horizon policies for risk-averse hydro-thermal planning," European Journal of Operational Research, Elsevier, vol. 217(1), pages 129-140.
    26. P. Girardeau & V. Leclere & A. B. Philpott, 2015. "On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 130-145, February.
    Full references (including those not matched with items on IDEAS)

    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:spr:eurjco:v:8:y:2020:i:2:d:10.1007_s13675-020-00123-y. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.