AbstractsMathematics

In the thesis we study the high frequency trading and its applications in limit order books. We discuss the basic concepts and review the models in the limit order books. The review section focuses on the queues in the limit order books, optimal trading strategies, short-term volatilities and multi-agent problems in the scenario of limit order markets. Discussions on the shortage of some prevalent models of limit order books are addressed thereafter. For the main results of the thesis, market data are calibrated to facilitate the comparison between a theoretical model and the empirical behaviors in terms of order flows, price changes and diffusion limit of prices.