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Inférence statistique pour l'optimisation stochastique : applications en finance et en gestion de production

Abstract : In this thesis, stochastic optimization problems are modelled and analyzed and we propose ways to solve these problems. In the first part, we consider asset allocation problems formulated as convex optimization problems. The cost function and the constraints depend on an unknown multidimensional parameter. We show, under quite general assumptions on the return process, and in particular under local time homogeneity, that we can construct a data-driven approximation of the original problem using an adaptive estimation of the unknown parameter. The accuracy of the approximate problem is given. This method has been applied on the VaR and Markowitz problems and we present the results of numerical experiments with simulated and real-world data. We then propose a sensitivity analysis for a class of quadratic problems which is used to propose a sensitivity analysis of the Markowitz problem. For this problem, we finally propose a stable calibration of the covariance matrix and robust counterparts.
In the second part, we analyse production management problems. We mainly deal with the problem of electricity production generation. We propose new modellings for this problem and ways of implementing them. One of the models we propose is solved using price decomposition. In this case, we show how to efficiently compute, by dynamic programming, the dual function. We finally explain, in each case, how a management strategy is determined. The different management methods are compared using real and simulated data.
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Contributor : Vincent Guigues <>
Submitted on : Monday, September 25, 2006 - 2:20:55 PM
Last modification on : Wednesday, March 10, 2021 - 1:50:03 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 1:09:59 AM


  • HAL Id : tel-00098287, version 1




Vincent Guigues. Inférence statistique pour l'optimisation stochastique : applications en finance et en gestion de production. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00098287⟩



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