Modeling, optimization and estimation for the on-line control of trading algorithms in limit-order markets

Abstract : This PhD thesis focuses on the quantitative analysis of mathematical problems arising in the field of optimal algorithmic trading. Concretely, we propose a scientific approach in order to optimize processes related to the capture and provision of liquidity in electronic markets. Because of the strongly industry-focused character of this work, not only we are interested in giving rigorous mathematical results but also to understand this research project in the context of the different stages that come into play during the practical implementation of the tools developed throughout the following chapters (e.g. model interpretation, parameter estimation, programming etc.).From a scientific standpoint the core of our work focuses on two techniques taken from the world of optimization and probability; these are, stochastic control and stochastic approximation. In particular, we provide original academic results for the problem of high frequency market making and the problem of portfolio liquidation by using limit orders; both by using a backward optimization approach. We also propose a forward optimization framework to solve the market making problem; the latter approach being quite innovative for optimal trading, as it opens the door for machine learning techniques.From a practical angle, this PhD thesis seeks to create a bridge between academic research and practitioners. Our mathematical findings are constantly put in perspective in terms of their practical implementation. Hence, we focus a large part of our work on studying the different factors that are of paramount importance to understand when transforming our quantitative techniques into industrial value: understanding the underlying market microstructure, empirical stylized facts, data processing, discussion about the models, limitations of our scientific framework etc.
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Joaquin Fernandez Tapia. Modeling, optimization and estimation for the on-line control of trading algorithms in limit-order markets. General Mathematics [math.GM]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066354⟩. ⟨tel-01266156⟩

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