Nonlinearity in high-frequency finance and optimal execution

In this thesis we consider two problems regarding the eld of market microstructure: the analysis and modeling of high frequency nancial data and the optimal execution of large orders. The rst problem is analyzed empirically within the context of the dynamics of limit order books. Such context imposes a discrete modeling approach about the variables of interest, like prices and bid-ask spreads. The optimal execution problem, instead, is analyzed within the context of a price model which allows for a nonlinear-transient market impact [43, 104]. Our interest is motivated by the fact that the study and implementation of optimal strategies is one of the main tasks of large banks and capital investment rms. The two problems are de ned by two di erent nonlinear models. A nonlinear modeling approach is necessary in order to reproduce the empirical data. Our work focuses on the analysis of the implications of such nonlinearities on the stochastic dynamics of prices and on optimal strategies. [...]