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...

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit...