Optimal Portfolio Liquidation and Stochastic Control with Singular State Constraints

Prof. Ulrich Horst

Humboldt University of Berlin

About the Speaker

Prof Horst is Professor of Applied Financial Mathematics at Humboldt University Berlin (HUB). He received his PhD in Mathematics form HUB in 2000. After his graduation he 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 Engineering at Princeton University, the Institute for Mathematical Economics at Bielefeld University, the Center for Mathematical Modelling at the Universidad de Chile, and the CEREMADE at the Paris Dauphine University. From July 2007 to June 2011 he was Scientific Director of the Deutsche Bank sponsored Quantitative Products Laboratory, and from March to August 2015, he was a Fellow at the Center for Interdisciplinary Research (ZIF) in Bielefeld. He was the Head of HUB’s the Mathematics Department for the last five years.

Abstract

Traditional financial market models assume that asset prices follow an exogenous stochastic process and that all transactions can be settled without any impact on market prices. This assumption is appropriate for small investors who trade only a negligible proportion of the average daily trading volume. It is not always appropriate for institutional investors trading large blocks of shares over a short time span. One of the main characteristics of stochastic optimisation problems arising in portfolio liquidation models is the singular terminal condition of the value function induced by the liquidation constraint. In these lectures we review three approaches to solve stochastic control problems with singular terminal state constraints: the penalization method, an asymptotic expansion technique, and forward-backward SDEs with undetermined terminal value. We illustrate the methods within the framework of two particular models: optimal liquidation with instantaneous price impact and stochastic resilience, and mean-field games of optimal portfolio liquidation.