Madhumita Paul, UNC Charlotte
Title: Brownian motion on spider type quantum graphs
Jiaming Chen, NYU Shanghai
Title: New stochastic Fubini theorem of measure-valued processes via stochastic integration
Classical stochastic Fubini theorems start from a fixed semimartingale S, say, and a family of integrands for S which are parametrized by a parameter z, say, from some parameter space Z. There is a (non- random) measure μ, say, on Z, and the stochastic Fubini theorem then says that integration with respect to μ and stochastic integration with respect to S can be interchanged. In other words, we can either 1) first integrate the parametrized integrands with respect to μ and then stochastically integrate the resulting process with respect to S, or we can 2) first stochastically integrate, for each z, the corresponding integrand with respect to S and then integrate the result with respect to μ – and both double integrals yield the same result. What happens now if we replace the fixed measure μ by a stochastic kernel from the predictable sigma- field to Z? Approach 1) still makes sense, but how about 2)? And can we still get some kind of stochastic Fubini theorem? We show that we can, but we need to define for that a stochastic integral, with respect to S, of suitable measure-valued processes. The origin of this question comes from a (still open) question in mathematical finance. There are also some connections to a class of Volterra-type semimartingales. Based on joint work with Tahir Choulli and Martin Schweizer.
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.