英文标题：
《A stochastic partial differential equation model for limit order book
dynamics》
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作者：
Rama Cont and Marvin S. Mueller
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最新提交年份：
2021
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英文摘要：
We propose an analytically tractable class of models for the dynamics of a limit order book, described through a stochastic partial differential equation (SPDE) with multiplicative noise for the order book centered at the mid-price, along with stochastic dynamics for the mid-price which is consistent with the order flow dynamics. We provide conditions under which the model admits a finite dimensional realization driven by a (low-dimensional) Markov process, leading to efficient estimation and computation methods. We study two examples of parsimonious models in this class: a two-factor model and a model with mean-reverting order book depth. For each model we analyze in detail the role of different parameters, the dynamics of the price, order book depth, volume and order imbalance, provide an intuitive financial interpretation of the variables involved and show how the model reproduces statistical properties of price changes, market depth and order flow in limit order markets.
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中文摘要：
我们提出了一类分析可处理的极限订单书动力学模型，该模型通过一个随机偏微分方程（SPDE）来描述，其中以中间价为中心的订单书具有乘性噪声，中间价的随机动力学与订单流动力学相一致。我们提供了模型允许由（低维）马尔可夫过程驱动的有限维实现的条件，从而产生了有效的估计和计算方法。我们研究了这类节俭模型的两个例子：一个双因素模型和一个具有均值回复订单深度的模型。对于每个模型，我们详细分析了不同参数的作用、价格动态、订单簿深度、数量和订单不平衡，对所涉及的变量提供了直观的财务解释，并展示了该模型如何再现限价订单市场中价格变化、市场深度和订单流的统计特性。
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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：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：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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