Optimal trading strategies with limit orders

A model is proposed to study optimal trading strategies in a limit order book, as typically arise when a trader has a block of shares to liquidate and she submits limit orders. The execution of limit orders is uncertain, which leads to a stochastic control problem. In contrast to previous literature, we allow the trader to choose both the quotes and the sizes of her submitted orders. Great 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, which is new in the literature on optimal trade execution where this problem is solved only in the case of market orders, and at the same time we offer guidelines to optimally place orders further behind the best price or to (re)position them more aggressively. Thus this paper is the first attempt towards a more realistic modeling of optimal liquidation throughout limit orders.