论文标题
快速和缓慢的最佳交易以及外在信息
Fast and Slow Optimal Trading with Exogenous Information
论文作者
论文摘要
我们考虑一个慢速的机构投资者和一个高频交易者之间的随机游戏，他们正在交易风险资产，而汇总订单流则影响资产价格。我们通过两个耦合的随机控制问题对该系统进行建模，其中高频交易者会更频繁地在价格预测信号上利用可用信息，但也受到定期的“末日”库存约束。鉴于机构投资者的任何可接受策略，我们首先得出了高频交易者的最佳战略。然后，鉴于高频交易者的最佳信号自适应策略，我们解决了机构投资者的问题，该策略是根据弗雷德霍尔姆积分方程的解决方程式解决的，从而确立了游戏的独特多处固定的stackelberg平衡。我们的结果为游戏提供了明确的解决方案，这表明高频交易者可以在每个时期采用掠夺性或合作策略，这取决于订单流和交易信号之间的权衡。我们还表明，当高频交易者的交易策略中考虑到高频交易者的订单流时，机构投资者的策略会更加有利可图。
We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.
