摘要翻译：
交易环境的演变导致了在不同场所交换相同金融工具的能力。由于流动性问题，贸易公司将大量订单分散在几个交易目的地，以优化其执行。为了解决这个问题，我们设计了两个随机递归学习过程，一个基于优化原理，另一个基于强化思想，来调整发送到不同场馆的订单比例。从理论的角度研究了这两个过程：我们证明了a.S.在输入数据处理的一些轻遍历（或“平均”）假设下，优化算法的收敛性。不需要马尔可夫属性。当输入是I.I.D。我们证明了收敛速度是由一个中心极限定理所决定的。最后，在模拟数据和真实数据上比较了两种算法的性能，比较了由一个事先知道各场馆执行数量的“内部人”设计的“甲骨文”策略的性能。
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英文标题：
《Optimal split of orders across liquidity pools: a stochastic algorithm
  approach》
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作者：
Sophie Laruelle (PMA), Charles-Albert Lehalle, Gilles Pag\`es (PMA)
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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：
  Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.
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PDF链接：
https://arxiv.org/pdf/0910.1166