Many securities markets are organized as double auctions where each incoming limit order --- i.e., an order to buy or sell at a specific price --- is stored in a data structure called the limit order book. A trade happens whenever a market order arrives --- i.e., an order to buy or sell at the...

We show that wealth processes in the block-shaped order book model of Obizhaeva/Wang converge to their counterparts in the reduced-form model proposed by Almgren/Chriss, as the resilience of the order book tends to infinity. As an application of this limit theorem, we explain how to reduce...