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

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 o...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Germany), 2013-06, Vol.77 (3), p.393-405
Main Authors: de Maere d’Aertrycke, Gauthier, Shapiro, Alexander, Smeers, Yves
Format: Article
Language:English
Subjects:
Approximation
Business and Management
Calculus of Variations and Optimal Control
Optimization
Dynamic programming
Electricity
Equipment costs
Lagrange multiplier
Lagrange multipliers
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Multistage
Operations research
Operations Research/Decision Theory
Original Article
Power plants
Risk
Risk exposure
Sampling techniques
Stochasticity
Studies
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Summary: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.
ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-012-0423-4