Online learning in limit order book trade execution

In this paper, we propose an online learning algorithm for optimal execution in the limit order book of a financial asset. Given a certain amount of shares to sell and an allocated time window to complete the transaction, the proposed algorithm dynamically learns the optimal number of shares to sell via market orders at pre-specified time-slots within the allocated time interval. We model this problem as a Markov Decision Process (MDP), which is then solved by dynamic programming. First, we prove that the optimal policy has a specific form, which requires either selling no shares or the maximum allowed amount of shares at each time slot. Then, we consider the learning problem, where the state transition probabilities are unknown and need to be learned on-the-fly. We propose a learning algorithm that exploits the form of the optimal policy when choosing the amount to trade. Our numerical results show that the proposed algorithm performs significantly better than the traditional Q-learning algorithm by exploiting the structure of the problem.