Mathematical Methods of Operations Research

, Volume 77, Issue 3, pp 393–405 | Cite as

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

  • Gauthier de Maere d’AertryckeEmail author
  • Alexander Shapiro
  • Yves Smeers
Original Article


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.


Lagrange Multiplier Cash Flow Stochastic Program Capacity Expansion Spot Market 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gauthier de Maere d’Aertrycke
    • 1
    Email author
  • Alexander Shapiro
    • 2
  • Yves Smeers
    • 3
  1. 1.Fondazione Eni Enrico MatteiMilanItaly
  2. 2.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Center for Operations Research and Econometrics, Department of Mathematical EngineeringUniversité catholique de LouvainLouvain-La-NeuveBelgium

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