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摘要翻译：
我们考虑了在限价订单书(LOB)中放置的大宗市场订单的最优执行策略。我们建立在Obizhaeva和Wang(2005)提出的弹性模型基础上，但允许通过给定的密度函数定义LOB的一般形状。因此，我们可以考虑经验观察到的LOB形状，并获得市场订单的非线性价格影响。我们区分了两种可能性来建模在一个大的市场订单之后的LOB的弹性：限价订单数量的指数恢复，即LOB的数量，或者买卖价差的指数恢复。我们考虑了这两种弹性模式，并在每种情况下导出了离散时间的显式最优执行策略。将我们的结果应用到块形LOB中，我们得到了最优策略的一个新的闭式表示，它显式地解决了Obizhaeva和Wang(2005)中给出的递归格式。对于形状函数和弹性类型的选择，我们也给出了最优策略鲁棒性的一些证据。
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英文标题：
《Optimal execution strategies in limit order books with general shape
functions》
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作者：
Aur\'elien Alfonsi (CERMICS), Antje Fruth, Alexander Schied
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最新提交年份：
2010
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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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英文摘要：
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.
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PDF链接：
https://arxiv.org/pdf/0708.1756
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