La programmation DC et DCA pour l'optimisation de portefeuille

Abstract : The topics presented in this thesis are related to new optimization techniques for solving some challenging problems resulting from finance. They are large-scale non convex optimization problems for which finding efficient solving methods is currently the topic of numerous researches. Our work is based mainly on DC (Difference of Convex functions) programming and DCA (DC Algorithm). This approach is motivated by the robustness and efficiency of DC programming and DCA approaches in comparison to the other methods. The thesis is divided into two parts and consists of seven chapters. In the first part entitled Methodology ; we present theoretical tools and algorithms that we are going to use in the thesis. The first chapter is about DC programming and DCA and the second focuses on branch and bound algorithms. In the second part we develop DC programming and DCA for solving some problems in finance. We begin with an introduction to the modern portfolio theory (The Chapter 3). The Chapter 4 is dedicated to the generalizations of the mean variance (MV) model of Markowitz, where we study the MV model under the buy-in threshold constraints, threshold constraints, and cardinality constraints. The Chapter 5 is devoted to the portfolio selection problem under downside risk measure and cardinality constraints. The Chapter 6 deals with the portfolio optimization under step increasing transaction costs functions. Finally, the robust investment strategies with discrete asset choice constraints are developed in the last chapter.
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Mahdi Moeini. La programmation DC et DCA pour l'optimisation de portefeuille. Economies et finances. Université Paul Verlaine - Metz, 2008. Français. ⟨NNT : 2008METZ008S⟩. ⟨tel-01752570⟩

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