英文标题：
《A diffusion approximation for limit order book models》
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作者：
Ulrich Horst and D\\\"orte Kreher
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最新提交年份：
2017
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英文摘要：
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an $\\R_+$-valued best bid price process and an $L^2_{loc}$-valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense.
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中文摘要：
本文推导了具有非线性状态相关订单到达和取消动态的离散时间单边极限订单簿模型序列的扩散近似。离散时间序列是根据$\\R\\u+$值的最佳投标价格过程和$^2\\u{loc}$-值的交易量过程来指定的。结果表明，在适当的假设下，插值离散时间模型的序列在局部意义上是相对紧的，并且任何极限点都满足一定的无限维SDE。在依赖结构的附加假设下，我们构造了两类适合一般框架的模型，使得极限SDE允许唯一解，从而离散动力学在局部意义上收敛到扩散极限。
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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：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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