High-Resilience Limits of Block-Shaped Order Books
  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 portfolio choice in highly-resilient Obizhaeva/Wang models to the corresponding problem in an Almgren/Chriss setup with small quadratic trading costs. 
Jan Kallsen, Johannes Muhle-Karbe
q-fin.TR math.OC math.PR q-fin.PM