英文标题：
《A buffer Hawkes process for limit order books》
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作者：
Ingemar Kaj and Mine Caglar
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最新提交年份：
2017
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英文摘要：
  We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process in which point process jumps generate a shot-noise intensity field. Unlike the Hawkes case, the intensity field is fed into a separate buffer, the size of which is the driving intensity of new jumps. In this manner, the intensity loop portrays mutual-excitation of point process events and buffer size dynamics. This scenario is directly applicable to the market evolution of limit order books, with buffer size being the current number of limit orders and the jumps representing the execution of market orders. We give a branching process representation of the point process and prove that the scaling limit is Brownian motion with explicit volatility.
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中文摘要：
我们引入了一个马尔可夫单点过程模型，通过缓冲机制调节随机强度，并通过自激效应控制到达缓冲区的流。该模型应用了霍克斯过程的原理，其中点过程跳跃产生散粒噪声强度场。与霍克斯的情况不同，强度场被送入一个单独的缓冲区，缓冲区的大小是新跳跃的驱动强度。通过这种方式，强度循环描述了点过程事件和缓冲区大小动态的相互激发。此场景直接适用于限额订单账簿的市场演变，缓冲区大小是当前限额订单的数量，跳跃代表市场订单的执行。我们给出了点过程的分支过程表示，并证明了标度极限是显式波动的布朗运动。
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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