Trading with Market Impact

Halil Soner

Professor of Mathematics, ETH Zürich
Senior Chair, Swiss Finance Institute

About the Speaker

Soner is currently a Professor at the Swiss Federal Institute of Technology in Zurich, Eidgenössische Technische Hochschule Zürich (ETH-Z) and also holds a senior chair at the Swiss Finance Institute. His research is on nonlinear analysis with emphasis on optimal stochastic control, partial differential equations, stochastic processes and mathematical finance.

Prior to moving to Zurich, he has spent nine years in Istanbul, Turkey and nineteen years in the United States of America. During his tenure in Turkey, he held the Isik Inselbag Chair at Sabanci University for two years and was a member of the Mathematics Department at Koc University for seven years prior to that. He has received his doctoral degree from the Division of Applied Mathematics of Brown University. Later, he was a member of the Department of Mathematical Sciences at Carnegie Mellon 1986 - 1998. In 1998, he became the Paul M. Wyhtes '55 Professor of Engineering and Finance at Princeton.

He has co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions, and authored or co-authored several articles on nonlinear partial differential equations, viscosity solutions, stochastic optimal control and mathematical finance. Since 2011, he has been the Executive Secretary of the Bachelier Finance Society and in 2014 he was awarded the Alexander von Humboldt Research Award.

About the Seminar

We consider a financial market in which our trading causes price impact and portfolio optimization in such markets. We propose several models for such markets using also resilience. We then study these models using stochastic optimization techniques. In particular, the classical dynamic programming equation approach provides equations that we analyse in several different asymptotic regimes.