Optimal control, statistical learning and order book modelling.

Summary The main objective of this thesis is to understand the interactions between financial agents and the order book. We consider in the first chapter the control problem of an agent trying to take into account the available liquidity in the order book in order to optimize the placement of a unit order. Our strategy reduces the risk of adverse selection. Nevertheless, the added value of this approach is weakened in the presence of latency: predicting future price movements is of little use if agents' reaction time is slow.In the next chapter, we extend our study to a more general execution problem where agents trade non-unitary quantities in order to limit their impact on the price. In the third chapter, we build on the previous approach to solve this time market making problems rather than execution problems. This allows us to propose relevant strategies compatible with the typical actions of market makers. Then, we model the behavior of directional high frequency traders and institutional brokers in order to simulate a market where our three types of agents interact optimally with each other.We propose in the fourth chapter an agent model where the flow dynamics depend not only on the state of the order book but also on the market history. To do so, we use generalizations of nonlinear Hawkes processes. In this framework, we are able to compute several relevant indicators based on individual flows. In particular, it is possible to classify market makers according to their contribution to volatility.To solve the control problems raised in the first part of the thesis, we have developed numerical schemes. Such an approach is possible when the dynamics of the model are known. When the environment is unknown, stochastic iterative algorithms are usually used. In the fifth chapter, we propose a method to accelerate the convergence of such algorithms.The approaches considered in the previous chapters are suitable for liquid markets using the order book mechanism. However, this methodology is not necessarily relevant for markets governed by specific operating rules. To address this issue, we propose, first, to study the behavior of prices in the very specific electricity market.