IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v77y2013i3p393-405.html
   My bibliography  Save this article

Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems

Author

Listed:
  • Gauthier Maere d’Aertrycke
  • Alexander Shapiro
  • Yves Smeers

Abstract

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We focus on the formulation with nonanticipativity constraints and show that their dual variables can be interpreted as the net margin accruing to plants in the different states of the world. We then propose a procedure to estimate the distribution of the Lagrange multipliers of the nonanticipativity constraints associated with first stage decisions; this gives us the distribution of the discounted cash flow of profitable plants in that stage. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Gauthier Maere d’Aertrycke & Alexander Shapiro & Yves Smeers, 2013. "Risk exposure and Lagrange multipliers of nonanticipativity constraints in multistage stochastic problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 393-405, June.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:3:p:393-405
    DOI: 10.1007/s00186-012-0423-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-012-0423-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-012-0423-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Alexander Shapiro, 2003. "Inference of statistical bounds for multistage stochastic programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 57-68, September.
    2. Andreas Ehrenmann & Yves Smeers, 2011. "Stochastic Equilibrium Models for Generation Capacity Expansion," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 273-310, Springer.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    2. Georg Pflug & Alois Pichler, 2015. "Dynamic generation of scenario trees," Computational Optimization and Applications, Springer, vol. 62(3), pages 641-668, December.
    3. Munoz, Francisco D. & van der Weijde, Adriaan Hendrik & Hobbs, Benjamin F. & Watson, Jean-Paul, 2017. "Does risk aversion affect transmission and generation planning? A Western North America case study," Energy Economics, Elsevier, vol. 64(C), pages 213-225.
    4. Mohseni, Soheil & Brent, Alan C. & Kelly, Scott & Browne, Will N., 2022. "Demand response-integrated investment and operational planning of renewable and sustainable energy systems considering forecast uncertainties: A systematic review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 158(C).
    5. Ambrosius, Mirjam & Egerer, Jonas & Grimm, Veronika & van der Weijde, Adriaan H., 2022. "Risk aversion in multilevel electricity market models with different congestion pricing regimes," Energy Economics, Elsevier, vol. 105(C).
    6. Rocha, Paula & Kuhn, Daniel, 2012. "Multistage stochastic portfolio optimisation in deregulated electricity markets using linear decision rules," European Journal of Operational Research, Elsevier, vol. 216(2), pages 397-408.
    7. de Maere d’Aertrycke, Gauthier & Ehrenmann, Andreas & Smeers, Yves, 2017. "Investment with incomplete markets for risk: The need for long-term contracts," Energy Policy, Elsevier, vol. 105(C), pages 571-583.
    8. Xiaotie Chen & David L. Woodruff, 2023. "Software for Data-Based Stochastic Programming Using Bootstrap Estimation," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1218-1224, November.
    9. Baker, Erin & Solak, Senay, 2011. "Climate change and optimal energy technology R&D policy," European Journal of Operational Research, Elsevier, vol. 213(2), pages 442-454, September.
    10. Agnieszka Konicz & David Pisinger & Alex Weissensteiner, 2015. "Optimal annuity portfolio under inflation risk," Computational Management Science, Springer, vol. 12(3), pages 461-488, July.
    11. Boris Defourny & Damien Ernst & Louis Wehenkel, 2013. "Scenario Trees and Policy Selection for Multistage Stochastic Programming Using Machine Learning," INFORMS Journal on Computing, INFORMS, vol. 25(3), pages 488-501, August.
    12. Sha, Yue & Zhang, Junlong & Cao, Hui, 2021. "Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 290(3), pages 886-900.
    13. Eyyüb Y. Kıbış & İ. Esra Büyüktahtakın & Robert G. Haight & Najmaddin Akhundov & Kathleen Knight & Charles E. Flower, 2021. "A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in Cities," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 808-834, May.
    14. Arnab Bhattacharya & Jeffrey P. Kharoufeh & Bo Zeng, 2023. "A Nonconvex Regularization Scheme for the Stochastic Dual Dynamic Programming Algorithm," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1161-1178, September.
    15. Xiaomin Xi & Ramteen Sioshansi, 2016. "A dynamic programming model of energy storage and transformer deployments to relieve distribution constraints," Computational Management Science, Springer, vol. 13(1), pages 119-146, January.
    16. P'ia Amigo & Sebasti'an Cea-Echenique & Felipe Feijoo, 2020. "An Emissions Trading System to reach NDC targets in the Chilean electric sector," Papers 2005.03843, arXiv.org.
    17. Senay Solak & Gustaf Solveling & John-Paul B. Clarke & Ellis L. Johnson, 2018. "Stochastic Runway Scheduling," Transportation Science, INFORMS, vol. 52(4), pages 917-940, August.
    18. Shin, Youngchul & Lee, Sangyoon & Moon, Ilkyeong, 2020. "Robust multiperiod inventory model considering trade-in program and refurbishment service: Implications to emerging markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    19. Acevedo, Giancarlo & Bernales, Alejandro & Flores, Andrés & Inzunza, Andrés & Moreno, Rodrigo, 2021. "The effect of environmental policies on risk reductions in energy generation," Journal of Economic Dynamics and Control, Elsevier, vol. 126(C).
    20. Maria Teresa Vespucci & Marida Bertocchi & Laureano F. Escudero & Stefano Zigrino, 2013. "A risk averse stochastic optimization model for power generation capacity expansion," Working Papers (2013-) 1305_qum, University of Bergamo, Department of Management, Economics and Quantitative Methods.

    More about this item

    Statistics

    Access and download statistics

    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:mathme:v:77:y:2013:i:3:p:393-405. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    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 (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.