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Apprentissage statistique en gestion de portefeuille : prédiction, gestion du risque et optimisation de portefeuille

Abstract : The goal of this work is to predict the returns of financial assets with statistical learning methods. We are motivated by the problem of stock selection in portfolio management. In particular, we will focus on the prediction of the sign of future returns at a given horizon. For this purpose, the methods cover the full range of problems from the design of training data to performance tests. The main contributions are both the full process addressing every step and the multitask Laplacian learning formulation that jointly solves for prediction tasks and their dependence structure. We first introduce the portfolio optimization framework and usually related approaches. We present the challenges for statistical learning and sound objectives for real-world application. The prediction process is made of four modules. The first module begins with data representation. We need a method for time series representation in order to process raw price data into robust and interpretable features as inputs for the supervised learning problem. The method is chosen to be piecewise linear approximation. Trees, built by the CART or dyadic Coifman-Wickerhauser algorithm, segment time series into homogeneous periods. The binary classification of returns then uses these features. We perform this learning task with a Random Forests procedure aggregating classification trees built by CART. We propose to add a reject option conditioned by tree-specific confidence scores, in order to reduce generalization risk. Multitask learning is then explored in the third module. We see dependent prediction tasks as the vertices of a graph, then propose an empirical risk minimization framework with the graph Laplacian as a penalty. Our method jointly solves for the tasks and their graph of relations. The last module defines the backtesting protocol corresponding to real conditions of use. Performance is assessed in this framework and the importance of parameter validation is stressed. This work has found concrete application in real-time financial recommendation. We conclude with a discussion on real performance in stock selection.
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Ruocong Zhang. Apprentissage statistique en gestion de portefeuille : prédiction, gestion du risque et optimisation de portefeuille. Apprentissage [cs.LG]. Télécom ParisTech, 2014. Français. ⟨NNT : 2014ENST0049⟩. ⟨tel-01856339⟩

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