中文摘要：

以连续竞价股票市场的限价订单簿为研究对象,将其看作一个多服务台的排队系统,每个价格档看作一个服务台,运用多维随机过程模拟限价订单簿上订单数目的演化.由于市场参与者的订单提交决策会受到限价订单簿深度的影响,因此引入状态依赖的泊松过程模拟限价订单流的到达和取消过程,即泊松过程的参数依赖于所处价格档上存量订单的数目.根据买卖中间价格改变的时刻对限价订单簿的动态演化分段进行研究,证明买卖中间价格改变前,限价订单簿内各个价格档上订单数目的发展变化服从生灭过程,并分别给出各生灭过程的转移概率和它们满足的Kolmogorov向后向前微分方程.而对于买卖中间价格发生变化的时刻,分析了不同类型的订单提交对最优买卖价格和各个价格档上订单数目的影响.

英文摘要：

The limit order book in continuous auction stock market could be viewed as a multi-server queueing system,where each price level was seen as a server.Then the limit order book could be modeled by a multi-dimensional random process.As order submission strategies of market participants often depended on the depth of limit order book,state-dependent Poisson processes were introduced to model the arrival and cancellation processes of limit order flows,namely the parameters of the Poisson processes depended on the state of limit order book.The dynamic evolution of limit order book driven by order flows was studied piecewise according to the moments of mid-price moves.The development of order quantity at each price level was proved to be a birth-death process before mid-price move.The transition probabilities and their Kolmogorov backward and forward differential equations of these birth-death processes were given.At the moment of mid-price move,the changes of bid/ask price and order quantity at each price level caused by different types of order submissions were analyzed.