Optimal Order Placement Using Markov Models of Limit Order Books

Abstract: We study optimal order placement in a limit order book. By modelling the limit order book dynamics as a Markov chain, we can frame the purchase of a single share as a Markov Decision Process. Within the framework of the model, we can estimate optimal decision policies numerically. The trade rate is varied using a running cost control variable. The optimal policy is found to result in a lower cost of trading as a function of the trade rate compared to a market order only strategy.