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

Summary The objective of this thesis is a quantitative study of the different mathematical problems that arise in algorithmic trading. Due to the strong applied character of this work, we are not only interested in the mathematical rigor of our results, but we also want to understand this research work in the context of the different steps that are part of the practical implementation of the tools that we develop. e.g. model interpretation, parameter estimation, computer implementation etc.From the scientific point of view, the core of our work is based on two techniques borrowed from the world of optimization and probability: stochastic control and stochastic approximation. In particular, we present original academic results for the high frequency market-making problem and the portfolio liquidation problem using limit-orders. Similarly, we solve the market-making problem using a forward optimization approach, which is innovative in the optimal trading literature as it opens the door to machine learning techniques. From a practical point of view, this thesis seeks to create a bridge between academic research and the financial industry. Our results are constantly considered from the perspective of their practical implementation. Thus, a large part of our work is focused on studying the different factors that are important to understand when transforming our quantitative techniques into industrial value: understanding the microstructure of the markets, stylized facts, data processing, model discussions, limitations of our scientific framework etc.