Limit order book modelling

本文的主要研究目标是建立基于非线性随机积分的极限序书模型的一般理论。该理论将包括最优执行、对冲、定价和排除套利的条件等问题的解决方案。连续时间模型的解决方案将导致对市场更好的理论理解，而离散时间模型的数值近似将使结果更适用，并将允许在实际数据上测量结果的性能。由于所有的模型都是一个一般模型的具体情况，所以所有的结果将被联系起来，因此，作为一个整体，它将创造一个更完整的理论。最优化问题的解和数值逼近将来自动态规划，而套期保值的理论结果将来自分解定理的推广和随机微积分的一般理论。几乎所有的股票都是通过电子平台交易的，因此，交易受到限价单结构的影响。更好地理解限价订单将改善交易策略和市场效率。

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.