标题： 带有预测信息的按比例分配微观结构中的最优高频交易 显示英文标题

标题： Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information

摘要： 我们提出了一种框架来研究在单跳比例优先限价订单簿中的最优交易策略，这通常出现在短期利率期货合约中。 高频交易者可以选择通过市价单或限价单进行交易，分别用脉冲控制和常规控制表示。 我们建模并讨论了这种特定微观结构的两个主要特征所导致的后果：首先，高频交易者发出的限价单只会部分成交，因此她无法控制成交的数量。为此，累计成交量由复合泊松过程建模。 其次，高频交易者面临过度交易风险，即库存发生剧烈变化的风险。这种风险的影响在最优清仓背景下进行了探讨。 最优交易问题通过随机控制和动态规划方法进行研究，这些方法导致价值函数以积分拟变分不等式的形式被刻画。 然后我们提供了相应的数值求解程序，并证明了这一计算方案的收敛性。 接下来，我们考察了几种可以简化数值程序的情况，同时关注了一些实际感兴趣的特殊情况。 我们在中位价格过程是鞅的情况下，研究了做市商问题和最佳执行问题。 我们也详细描述了一个高频交易策略，当可获得（预测性）中位价格方向信息时。 每种策略都通过数值测试进行说明。 显示英文摘要

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.