Michael Grabchak

Vlad Margarint, UNC Charlotte

Title: Introduction to Schramm-Loewner Evolutions theory and continuity in a natural parameter

Abstract:  Schramm-Loewner Evolution (SLE) was introduced in 2000 by Oded Schramm in order to give meaning to scaling limits of interfaces of some models of Planar Statistical Physics. In the last few years, there were many models that were proven to have their interfaces in the scaling limit described by SLE. The SLE curves are studied through the Loewner Differential Equation with a Brownian motion driver. In the first part of the talk, I will introduce SLE theory. In the second part, I aim to present results of mine and collaborators on the continuity of this model in a natural parameter. If time permits, I will also touch on extensions of this model to multiple SLE curves. 

Sébastien Bossu, UNC Charlotte

Title: Spanning multi-asset option payoffs with ReLUs and Radon transforms

Abstract: The Carr-Madan spanning formula which underlies the calculation of the VIX gives a decomposition of an arbitrary payoff function as a sum of calls and puts. This formula can be generalized to multi-asset option using Radon transforms, and the corresponding inverse problem can be approximated numerically using one hidden-layer feedforward ReLU neural networks (NN). In the first part of this talk, the NN approach is used to identify static hedges (“spanning portfolios”) for a selection of multi-asset options, such as best-of calls or dispersion puts, using basket payoffs that are easier to trade and price. In the second part of this talk, perfect static hedges based on (suitably regularized) Radon transform solutions are discussed. (Joint work with Stéphane Crépey, Univ. Paris-Cité, and his PhD students Nisrine Madhar and Hoang-Dung Nguyen, Univ. Paris-Cité and Natixis)

Bio: Sébastien Bossu received his Ph.D. in quantitative finance from Université Paris-Saclay in 2022 under the guidance of Peter Carr, Stéphane Crépey and Andrew Papanicolaou. He has published 3 articles in top academic journals as well as two textbooks and several industry papers in mathematical finance, including the popular read “Just What You Need to Know About Variance Swaps” which circulated widely. Sébastien previously served as part-time faculty at Fordham University, Pace University, Johns Hopkins Carey Business School, NYU Courant and Boston University Questrom School of Business, and most recently as full-time Visiting Professor of Finance at WPI Business School. He is a regular speaker at regional, national and international conferences in his field. Sébastien is also a graduate from The University of Chicago, HEC Paris, Columbia University and Sorbonne Université (fmr. Pierre-et-Marie-Curie).

Prior to his Ph.D., Sébastien was principal at his startup investment and consulting company in New York City since 2011, and worked at JPMorgan and Dresdner Kleinwort (now Commerzbank) in London between 2003 and 2008. As a young Analyst at JPMorgan, he discovered the correlation proxy formula and was the first author to establish the connection between dispersion trading and correlation swaps.

Michael Grabchak, UNC Charlotte

Title: The Test And Find Problem (Joint work with X. Li and I. Sonin)

Stanislav Molchanov, UNC Charlotte

Title: Collisions between two random sequences

Stanislav Molchanov, UNC Charlotte

Title: The collisions between random and non-random sequences

Stanislav Molchanov, UNC Charlotte

Title: Entropy, Kolmogorov’s complexity and optimal simulation of the random variables

Stanislav Molchanov, UNC Charlotte

Title: Furstenberg theorem and its applications in spectral theory Part II

Stanislav Molchanov, UNC Charlotte

Title: Furstenberg theorem and its applications in spectral theory

Oleg Safronov, UNC Charlotte

Title: Jean Bourgain’s problem about a multi-dimensional random Schrödinger operator. Obtaining new results under weaker assumptions.

Mark Freidlin, University of Maryland

Title: Long-Time Influence of Small Perturbations

Abstract: Long-time influence of small deterministic and stochastic perturbations can be described as a motion on the simplex of invariant probability measures of the non-perturbed system. I will demonstrate this general approach in the case of  perturbations of a stochastic system with multiple stationary regimes. If the system has a first integral, the long–time behavior of the perturbed system, in an appropriate time scale, can be described by a motion on the Reeb graph of the first integral. This is a modified (because of the interior vertices of the Reeb graph)  averaging-principle-type result. If the non-perturbed stochastic system has just a finite number of ergodic invariant probability measures, the long-time behavior is defined by limit theorems for large deviations.