Optimal High Frequency Interactions with Orderbook

We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity... [ view full abstract ]

We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders and cancellations. To solve the agent's control problem we build an orderbook model and optimize an expected utility function based on our price impact. We derive the equations satisfied  by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution strategies.