Order book modeling and liquidity risk management.

Summary This thesis deals with the study of stochastic order book modeling, and two stochastic control problems in a context of liquidity risk and impact on asset prices. The thesis is composed of two distinct parts.In the first part, we treat, under different aspects, a Markovian order book model.In particular, in chapter 2, we introduce a cumulative depth representation model. We consider different types of event arrivals with a dependence on the current state.Chapter 3 deals with the model stability problem through a semi-martingale approach for the classification of a countable Markov chain. We give, for each classification problem, a calibration of the model from empirical facts such as the average order book density profile.Chapter 4 is devoted to the estimation and calibration of our model from market data streams. Thus, we compare our model and the data using stylized facts and empirical facts. We give a concrete calibration to the different classification problems.Then, in chapter 5, we treat the optimal liquidation problem within the framework of the cumulative depth representation model.In the second part, we propose a modeling of an investor's optimal liquidation problem with stochastic resilience. We reduce the problem to a singular stochastic control problem. We show that the associated value function is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. Moreover, we use an iterative numerical method to compute the optimal strategy. The convergence of this numerical scheme is obtained via monotonicity, stability and consistency criteria.