AQFC2015

Seminar: Second Order Approximations for Limit Order Books

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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

 

Date: 
Thursday, September 14, 2017 - 16:30 to 17:30