We incorporate a Markovian signal in the optimal trading framework which was initially proposed by Gatheral et al. (Math. Finance 22:445–474, 2012) and provide results on the existence and uniqueness of an optimal trading strategy. Moreover, we derive an explicit singular optimal strategy for the special case of an Ornstein–Uhlenbeck signal and an exponentially decaying transient market impact. The combination of a mean-reverting signal along with a market impact decay is of special interest, since they affect the short term price variations in opposite directions. Later, we show that in the asymptotic limit where the transient market impact becomes instantaneous, the optimal strategy becomes continuous. This result is compatible with the optimal trading framework which was proposed by Cartea and Jaimungal (Appl. Math. Finance 20:512–547, 2013). In order to support our models, we analyse nine months of tick-by-tick data on 13 European stocks from the NASDAQ OMX exchange. We show that order book imbalance is a predictor of the future price move and has some mean-reverting properties. From this data, we show that market participants, especially high-frequency traders, use this signal in their trading strategies.

中文翻译：

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将信号纳入最佳交易

我们将马尔可夫信号纳入最佳交易框架，该框架最初由Gatheral等人提出。（Math。Finance 22：445–474，2012），并提供关于最佳交易策略的存在和唯一性的结果。此外，我们针对Ornstein–Uhlenbeck信号的特殊情况以及呈指数衰减的瞬态市场影响，导出了一个显式的奇异最优策略。均值回复信号与市场影响衰减的组合特别受关注，因为它们会影响相反方向的短期价格波动。后来，我们表明，在瞬态市场影响变为瞬时的渐近极限中，最优策略变得连续。此结果与Cartea和Jaimungal提出的最佳交易框架兼容（Appl。Math。Finance 20：512–547，2013）。为了支持我们的模型，我们分析了来自纳斯达克OMX交易所的13支欧洲股票的9个月的逐笔价格数据。我们表明，订单簿不平衡是未来价格走势的预测因素，并且具有一定的均值回复特性。从这些数据可以看出，市场参与者，尤其是高频交易者，在其交易策略中使用了该信号。