  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 order book 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.
