  Optimal trade execution is an important problem faced by essentially all
traders. Much research into optimal execution uses stringent model assumptions
and applies continuous time stochastic control to solve them. Here, we instead
take a model free approach and develop a variation of Deep Q-Learning to
estimate the optimal actions of a trader. The model is a fully connected Neural
Network trained using Experience Replay and Double DQN with input features
given by the current state of the limit order book, other trading signals, and
available execution actions, while the output is the Q-value function
estimating the future rewards under an arbitrary action. We apply our model to
nine different stocks and find that it outperforms the standard benchmark
approach on most stocks using the measures of (i) mean and median
out-performance, (ii) probability of out-performance, and (iii) gain-loss
ratios.
