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                   Department of Systems Engineering and Engineering Management

                                The Chinese University of Hong Kong





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Date: Thursday, 4:30pm - 5:30pm, 14 September, 2017



Title: Second Order Approximations for Limit Order Books



Speaker: ULRICH HORST, Department of Mathematics, Humboldt-Universität zu Berlin



Abstract:

In this paper we derive a second order approximation for an infinite

dimensional limit order book model, in which the dynamics of the

incoming order flow is allowed to depend on the current market price

as well as on a volume indicator (e.g. the volume standing at the top

of the book). We study the fluctuations of the price and volume

process relative to their first order approximation given in ODE-PDE

form under two different scaling regimes. In the first case we suppose

that price changes are really rare, yielding a constant first order

approximation for the price. This leads to a measure valued SDE driven

by an infinite dimensional Brownian motion in the second order

approximation of the volume process. In the second case we use a

slower rescaling rate, which leads to a non-degenerate first order

approximation and gives a PDE with random coefficients in the second

order approximation for the volume process.





Biography:

After graduating with a PhD in Mathematics from Humboldt-Universität

zu Berlin in 2000, Ulrich Horst spent several years teaching in

Germany and North America. Before he returned to Berlin in the summer

of 2007 he was an Assistant Professor at the department of mathematics

at the University of British Columbia in Vancouver. Ulrich Horst held

visiting positions at various institutions including the Departments

Economics and of Operations Research and Financial Enginnering at

Princeton University, the Institute for Mathematical Economics at

Bielefeld University, the Center for Mathematical Modelling at the

Universidad de Chile, the CEREMADE at the Universite Paris Dauphine,

and the Risk Management Institute at the National University of

Singapore. From March - August 2015 he was a Fellow at the Center for

Interdisciplinary Research (ZIF) in Bielefeld.



Ulrich Horst was Deutsche Bank Professor of Applied Mathematical

Finance at Humboldt-Universität and the Scientific Director of the

Deutsche Bank sponsored Quantitative Products Laboratory. From 07/2012

- 05/2014 he served on the board of the DFG Research Center

Mathematics for Key Technologies. During this time he was also

scientist in charge of its Application Area E. He was principal

investigator of Project A11 of the SFB 649 "Economic Risk" and a board

member of the IRTG 1846 "Stochastic Analysis with applications to

Biology, Finance and Physics". Currently he is principal investigator

of Project B2 of the TR CRC 190 ``Rationality and Competition''. He is

affiliated with the School of Business and Economics at Humboldt

University. Since 04/13 he is Head of the Mathematics Department.





Everyone is welcome to attend the talk!



Venue: Room 513,William M.W. Mong Engineering Building

(ERB),(Engineering Building Complex Phase 2) The Chinese University of

Hong Kong.



The talk will be hosted by:

Prof. Gao Xuefeng,

Department of Systems Engineering and Engineering Management,

The Chinese University of Hong Kong,

E-mail: xfgao@se.cuhk.edu.hk

Homepage: http://www.se.cuhk.edu.hk/people/xfgao.html



SEEM-5201 Website: http://seminar.se.cuhk.edu.hk

Email: seem5201@se.cuhk.edu.hk