Fast and Slow Optimal Trading with Exogenous Information

We model the interaction between a slow institutional investor and a high-frequency trader as a stochastic multiperiod Stackelberg game. The high-frequency trader exploits price information more frequently and is subject to periodic 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 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 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 more profitable when the order-flow of the high-frequency trader is taken into account