摘要翻译：
我们提出了一个框架来研究最优交易策略在一个滴答按比例限价指令书，典型地出现在短期利率期货合约。高频交易者可以选择通过市场指令或限价指令进行交易，分别用脉冲控制和规则控制表示。我们建模并讨论了这种特殊微观结构的两个主要特征的后果：第一，高频交易者发送的限价指令只被部分执行，因此她无法控制执行的数量。为此目的，累积执行量模型由复合泊松过程。第二，高频交易者面临过度交易风险，即库存剧烈变动的风险。这种风险的后果将在最优清算的背景下进行调查。利用随机控制和动态规划的方法研究了最优交易问题，并用积分拟变分不等式刻画了最优交易问题的价值函数。然后给出了相应的数值解法，并证明了该计算格式的收敛性。接下来，我们考察了几种情况，在这些情况下，我们一方面可以通过减少状态变量的数量来简化数值过程，另一方面可以关注实际感兴趣的具体情况。在中间价格过程是鞅的情况下，我们研究了一个做市问题和一个最佳执行问题。我们还详细介绍了一个高频交易策略的情况下，一个（预测）方向信息的中间价是可用的。通过数值试验说明了所得到的每一种策略。
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英文标题：
《Optimal High Frequency Trading in a Pro-Rata Microstructure with
  Predictive Information》
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作者：
Fabien Guilbaud (LPMA), Huy\^en Pham (LPMA, CREST)
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最新提交年份：
2012
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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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英文摘要：
  We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic programming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.
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PDF链接：
https://arxiv.org/pdf/1205.3051