英文标题：
《Ergodicity and diffusivity of Markovian order book models: a general
  framework》
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作者：
Weibing Huang and Mathieu Rosenbaum
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最新提交年份：
2015
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英文摘要：
  We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic features of financial assets. To do so, we propose a new method of order book representation, and decompose the problem of order book modeling into two sub-problems: dynamics of a continuous-time double auction system with a fixed reference price; interactions between the double auction system and the reference price movements. State dependency is included in our framework by allowing the order flow intensities to depend on the order book state. Furthermore, contrary to most existing models, the impact of the order book updates on the reference price dynamics is not assumed to be instantaneous. We first prove that under general assumptions, our system is ergodic. Then we deduce the convergence towards a Brownian motion of the rescaled price process.
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中文摘要：
我们提出了一个通用的马尔可夫订单建模框架。通过我们的方法，我们旨在提供一种工具，使我们能够更好地了解价格形成过程以及金融资产微观和宏观特征之间的联系。为此，我们提出了一种新的订单书表示方法，并将订单书建模问题分解为两个子问题：具有固定参考价格的连续时间双拍卖系统的动力学；双重拍卖系统与参考价格变动之间的相互作用。通过允许订单流强度依赖于订单簿状态，我们的框架中包含了状态依赖性。此外，与大多数现有模型相反，订单簿更新对参考价格动态的影响不是瞬时的。我们首先证明，在一般假设下，我们的系统是遍历的。然后我们推导了重新标度价格过程的布朗运动收敛性。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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