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We consider a stochastic game between a slow institutional investor and ahigh-frequency trader who are trading a risky asset and their aggregatedorder-flow impacts the asset price. We model this system by means of twocoupled stochastic control problems, in which the high-frequency traderexploits the available information on a price predicting signal morefrequently, but is also subject to periodic "end of day" inventory constraints.We first derive the optimal strategy of the high-frequency trader given anyadmissible strategy of the institutional investor. Then, we solve the problemof the institutional investor given the optimal signal-adaptive strategy of thehigh-frequency trader, in terms of the resolvent of a Fredholm integralequation, thus establishing the unique multi-period Stackelberg equilibrium ofthe game. Our results provide an explicit solution to the game, which showsthat the high-frequency trader can adopt either predatory or cooperativestrategies in each period, depending on the tradeoff between the order-flow andthe trading signal. We also show that the institutional investor's strategy isconsiderably more profitable when the order-flow of the high-frequency traderis taken into account in her trading strategy.

Fast and Slow Optimal Trading with Exogenous Information