Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience

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

We study an optimal execution problem in illiquid markets with both instantaneous and persistent price impact and stochastic resilience when only absolutely continuous trading strategies are admissible. In our model the value function can be described by a three- dimensional system of backward stochastic differential equations (BSDE) with a singular terminal condition in one component. We prove existence and uniqueness of a solution to the BSDE system and characterize both the value function and the optimal strategy in terms of the unique solution to the BSDE system. Our existence proof is based on an asymptotic expansion of the BSDE system at the terminal time that allows us to express the system in terms of a equivalent system with finite terminal value but singular driver. The talk is based on joint work with Paulwin Graewe (Humboldt University of Berlin).

This is a joint seminar with Centre for Quantitative Finance.