Inverse Problems in Finance
Welcome back to the spring 2017 semester. We have an exciting list of guest speakers coming to visit this spring. These talks will be held on different days of the week to allow everyone an opportunity to attend.
On Monday, January 30th at 2PM in LC 400, our first invited guest, Dr. Sergey Nadtochiy, Assistant Professor in the Department of Mathematics at the University of Michigan will give a talk on the following topic:
Title: Inverse Problems in Finance
In this talk, I present several important problems arising in Quantitative Finance, unified by their interpretation as Inverse Problems for Parabolic Partial Differential Equations. The main difficulties associated with such problems stem from their ill-posedness: even if a solution exists, it does not depend continuously on the input data. This, in turn, makes it very challenging (or even impossible) to solve such a problem numerically: the natural numerical approximations, typically, do not converge. In order to overcome these challenges, in my joint works with P. Carr, M, Tehranchi, and E. Bayraktar, we develop analytical solutions to these inverse problems. The mathematical techniques used in the course of this work range from the purely geometric arguments to the methods of Probability Theory, Partial Differential Equations, Complex and Fourier Analysis, and Potential Theory. The solutions to these inverse problems have several applications in Finance, Physics, and Computational Methods. In particular, we use these results to develop an Exact Calibration algorithm for European Options, a Static Hedging strategy for Barrier Options, a Trading Strategy for Implied Skew, and a general description of solutions to Optimization Problems with Infinite Time Horizon.
Dr. Sergey Nadtochiy holds the position of an Assistant Professor in the Department of Mathematics at the University of Michigan since 2012. His research interests are in the field of Financial Mathematics and Engineering, including the problems of Pricing and Hedging of Derivative Contracts, Volatility Modeling, Optimal Investment, and Market Microstructure. Sergey strives to solve practically relevant problems using the methods of Probability Theory, Partial Differential Equations, Optimal Control, and Game Theory.
Sergey received his Bachelor’s degree (summa cum laude) from the Department of Mathematics and Mechanics in the Moscow State University, in 2005. He continued his education at a graduate level in the Department of Operations Research and Financial Engineering at Princeton University, receiving his Ph.D. degree in 2009. Upon graduation, Sergey joined the Oxford-Man Institute for Quantitative Finance, in the University of Oxford, where he held the position of a Senior Research Fellow in 2009-2012. In addition, Sergey has worked as a Researcher in Quantitative Finance at Bloomberg L.P., in 2007, and as a Quantitative Researcher in the Proprietary Positioning Business at JPMorgan & Chase, in 2008.
Please mark your calendars! Refreshments will be served. We look forward to seeing you at this lecture.