Diffusion scaling of a limit-order book model
Steven Shreve (Carnegie Mellon University, USA)
Joint work with Christopher Almost and John Lehoczky

Thursday June 5, 09:00-10:00 | session I8 | Plenary session | room AB

With the movement of trading away from the trading floor onto electronic exchanges - and the accompanying rise in the volume of order submission - has come an increase in the need for tractable mathematical models of the whole limit order book. The problem is inherently high-dimensional and the most natural description of the dynamics of the order flows has them depend on the state of the book in a discontinuous way. We examine a popular discrete model from the literature and describe its limit under a diffusion scaling inspired by queueing theory. Interesting features include a process that is either "frozen" or diffusing according to whether another diffusion is positive or negative.