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英文标题：
《A law of large numbers for limit order books》
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作者：
Ulrich Horst and Michael Paulsen
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最新提交年份：
2015
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英文摘要：
We define a stochastic model of a two-sided limit order book in terms of its key quantities \\textit{best bid [ask] price} and the \\textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps the expected volume rate over the considered price interval invariant, we prove a limit theorem. The limit theorem states that, given regularity conditions on the random order flow, the key quantities converge in probability to a tractable continuous limiting model. In the limit model the buy and sell volume densities are given as the unique solution to first-order linear hyperbolic PDEs, specified by the expected order flow parameters.
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中文摘要：
我们定义了一个双边限价订单簿的随机模型，它的关键数量是{textit{best bid[ask]price}和{textit{standing buy[sell]volume density}。对于离散参数的简单标度，即在所考虑的价格区间内保持预期容积率不变，我们证明了一个极限定理。极限定理表明，给定随机序流的正则性条件，关键量以概率收敛到一个可处理的连续极限模型。在极限模型中，买卖体积密度作为一阶线性双曲偏微分方程的唯一解给出，由期望阶流参数指定。
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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：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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