Portfolio Liquidation under Market Impact

Prof. Ulrich Horst

Humboldt University of Berlin

About the Speaker

After graduating with a PhD in Mathematics from Humboldt University of 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 and at CEREMADE, Universite Paris Dauphine. 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 is 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" and a member of the School of Business and Economics at Humboldt University. Since April 2013, he is Head of the Mathematics Department.

About the Seminar

Traditional financial market models assume that all transactions can be settled at prevailing prices without any impact on market dynamics. This assumption is appropriate for small investors but it is not always appropriate for institutional investors trading large blocks of shares over a short time span. The analysis of optimal liquidation problems has received considerable attention in the mathematical finance and stochastic control literature in recent years. One of the main characteristics of stochastic optimization problems arising in portfolio liquidation models is the singular terminal condition of the value function (and hence the HJB equation characterising is) induced by the liquidation constraint. In this talk we review various approaches to optimal portfolio liquidation and discuss some of the mathematical challenges arising in such models.