英文标题：
《Second order approximations for limit order books》
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作者：
Ulrich Horst and D\\\"orte Kreher
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最新提交年份：
2018
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英文摘要：
  In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g.~the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE-PDE form under two different scaling regimes. In the first case we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite dimensional Brownian motion in the second order approximation of the volume process. In the second case we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.
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中文摘要：
在本文中，我们推导了无限维极限订单簿模型的二阶近似值，在该模型中，传入订单流的动态取决于当前的市场价格以及数量指标（例如，位于账簿顶部的数量）。我们研究了在两种不同的标度制度下，价格和交易量过程相对于ODE-PDE形式给出的一阶近似值的波动。在第一种情况下，我们假设价格变化非常罕见，从而得出价格的恒定一阶近似值。这导致在体积过程的二阶近似下，由无限维布朗运动驱动的测度值SDE。在第二种情况下，我们使用较慢的重缩放率，这导致了非退化一阶近似，并给出了体积过程二阶近似下具有随机系数的偏微分方程。我们的结果可用于推导市场影响下最优投资组合清算模型的置信区间。
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分类信息：

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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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：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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