Limit order book modelling

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The main goal of my research is to build a general theory for limit order book models based on nonlinear stochastic integrals. This theory will include solutions for the problems of optimal execution, hedging, pricing and conditions to rule out arbitrage. Solutions for continuous time models will lead to a better theoretical understanding of the markets while numerical approximations for discrete time models will make the results more applicable and will allow to measure the performance of the results on real data. Since all the models are specific cases of a general model, all the results will be linked and, therefore, as a whole, it will create a more complete theory. Solutions and numerical approximations to optimization problems will come from dynamic programming while theoretical results for hedging will come from the extension of decomposition theorems and the general theory of stochastic calculus. Almost all stocks are traded through electronic platforms, and therefore, transactions are affected by the structure of limit order books. A better understanding of limit order book will improve trading strategies and market efficiency.