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Sensitivity analysis of energy contracts by stochastic programming techniques. (English) Zbl 1269.90070
Carmona, René A. (ed.) et al., Numerical methods in finance. Selected papers based on the presentations at the workshop, Bordeaux, France, June 2010. Berlin: Springer (ISBN 978-3-642-25745-2/hbk; 978-3-642-25746-9/ebook). Springer Proceedings in Mathematics 12, 447-471 (2012).
Summary: We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged whilst state variable is multi-dimensional. In [the authors, Ann. Oper. Res. 200, 199–222 (2012; Zbl 1254.90132)], we proposed an algorithm to deal with such a problem, based on quantization of the random process and a dual dynamic programming type approach. We obtained accurate estimates of the optimal value and a suboptimal strategy from this algorithm. In this paper, we analyse the sensitivity with respect to parameters driving the price model. We discuss the estimate of marginal price based on the Danskin’s theorem. Finally, some numerical results applied to realistic energy market problems have been performed. Comparisons between results obtained in [loc. cit.] and other classical methods are provided and give evidence of the good accuracy of the estimate of marginal prices.
For the entire collection see [Zbl 1238.91005].

MSC:
90C15 Stochastic programming
90C31 Sensitivity, stability, parametric optimization
91G60 Numerical methods (including Monte Carlo methods)
91G99 Actuarial science and mathematical finance
49Q12 Sensitivity analysis for optimization problems on manifolds
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
49L20 Dynamic programming in optimal control and differential games
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