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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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