Optimal trading strategies with limit orders

A model is proposed to study the risk management problem of designing optimal trading strategies in a limit order book. The execution of limit orders is uncertain, which leads to a stochastic control problem. In contrast to previous literature, we allow the agents to choose both the quotes and the sizes of their submitted orders. Attention is paid to how the trading strategy is affected by an order book’s characteristics, market volatility and the trader’s risk attitude. We prescribe an optimal splitting of the order size for the trades with limit orders, while the existing literature offers a solution to this problem with market orders, and, at the same time, we provide guidelines to optimally place 27 orders further behind the best price or to (re)position them more aggressively. Thus this 28 paper is an attempt towards a more realistic modeling of optimal liquidation throughout 29 limit orders.