Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience

  Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience Prof Ulrich Horst, Head, Department of Mathematics; Humboldt-University Berlin Date: 01 Mar 2017 Time: 10.30am – 12.00pm Venue: I-cube building, Executive Seminar Room Level 4 (This seminar is organized jointly with the Risk Management Institute)

About the Speaker

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.

Abstract

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 (HU Berlin).