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  Issue 21 | Archive November 2014

Prof. Steven Shreve Discusses Diffusion Scaling of a Limit-order Book Model

On 11 September, Prof. Steven Shreve, Orion Hoch University Professor of Mathematics at Carnegie Mellon University (CMU), gave a talk entitled ¡°Diffusion Scaling of a Limit-order Book Model¡± to more than 120 participants.

Against the backdrop of trading away from the trading floor onto electronic exchanges ¨C and the accompanying rise in the volume of order submission ¨C has come an increase in the need for tractable mathematical models of the whole limit order book, Prof. Shreve noted. He found 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.

Organized by the NUS Finance and Risk Management Cluster, and jointly hosted by the RMI and Centre for Quantitative Finance, the talk featured the ongoing collaboration of Prof. Steven Shreve, Christopher Almost and John Lehoczky.

The talk¡¯s goal is to ¡°build a ¡®zero-intelligence¡¯ Poisson model of the limit-order book and determine its diffusion limit,¡± shared the co-founder of CMU¡¯s Master's degree in Computational Finance. In the model, there is ¡°no strategic play¡± by the agents submitting orders, according to him. Interesting features include a process that is either "frozen" or diffusing according to whether another diffusion is positive or negative.

The author of award-winning book Stochastic Calculus for Finance, Prof. Shreve has also been a faculty member of the University of California at Berkeley and Massachusetts Institute of Technology.

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Published quarterly by Risk Management Institute, NUS
Editor: Ivy Wang (rmiwy@nus.edu.sg)