Iryna Kashuba

Shenzhen International Center for Mathematics and Southern University of Science and Technology, Shenzhen, China 

Iryna Kashuba got her Bachelor degree from Taras Shevchenko Kyiv University in 1997, Master degree from Kaiserslautern University in 2000, and her PhD degree from São Paulo University in 2004. She did her postdoc at Centre de Recherches Mathématiques of University of Montreal  and at the University of California, Berkeley.

For more than 15 years Iryna worked at University of  São Paulo in Brazil and since last May she is working at the International Center for Mathematics at SUSTech, China. 

Her mathematical interests are in structure and representation theory of Lie and Jordan algebras and superalgebras.

Title: Representation type of Jordan (super)algebras 

Abstract: We will review recent and classical results on the representations of finite dimensional Jordan algebras and superalgebras. We will weigh the pros against the cons of using the Tits-Kantor-Koecher construction for this problem. This is joint work with Vera Serganova. 

Alexander Lipton

Global Head, Research and Development, ADIA
Advisory Board Member, ADIA Lab

Professor of Practice, Khalifa University

Alexander Lipton is Global Head, Research & Development at Abu Dhabi Investment Authority, Professor of Practice at Khalifa University, Visiting Professor and Dean’s Fellow at the Hebrew University of Jerusalem, Connection Science Fellow at MIT, and Advisory Board member at ADIA Lab. Alex is a Co-Founder of Sila, a company providing, digital wallet & ACH payment services, and an advisory board member at several fintech companies worldwide. From 2006–2016, Alex was Co-Head of the Global Quantitative Group and Quantitative Solutions Executive at Bank of America. Earlier, he was a senior manager at Citadel, Credit Suisse, Deutsche Bank, and Bankers Trust. In addition, Alex held visiting professorships at EPFL, NYU, Oxford University, Imperial College, and the University of Illinois. Before becoming a quant, Alex was a Full Professor of Mathematics at the University of Illinois and a Consultant at the Los Alamos National Laboratory. Risk Magazine awarded him the Inaugural Quant of the Year Award in 2000 and the Buy-side Quant of the Year Award in 2021. Alex authored/edited twelve books and more than a hundred scientific papers on nuclear fusion, astrophysics, applied mathematics, financial engineering, and distributed ledgers. He frequently gives keynote presentations on Quantitative Finance and FinTech at conferences and forums worldwide. 

Title: Hydrodynamics of Markets: Hidden Links Between Physics and Finance  

Abstract: We have found intriguing links between a wide range of physics and financial engineering topics that, at first glance, have little in common. All these problems can be reduced to solving affine differential and pseudo-differential equations (PDEs and PPDEs). This task involves solving a set of ordinary differential equations parametrically dependent on time-varying wave vectors and piecing their solutions together. Affine PDEs and PPDEs are a natural fit for modelling dynamic systems across various science and math fields.

We have drawn connections across different areas, linking phenomena like the small wave-like perturbations of linear fluid flows, known in hydrodynamics as Kelvin waves, to the movements of particles described in molecular physics by the Kolmogorov and Klein-Kramers equations, to Gaussian and non-Gaussian processes like the Ornstein-Uhlenbeck and Feller processes, which pop up in both physics and financial engineering. Using Kelvin waves as a tool, we have developed a unified math framework to create transition probability density functions that apply to physics and financial engineering challenges. 

One interesting finding from our work is that the original solution to the Kolmogorov equation had a mistake, which we have fixed. Our approach is versatile, covering many phenomena, from regular and jump diffusions to Lévy processes and anomalous diffusions and beyond. It is handy for exploring various financial engineering concepts, including well-known models like Black-Scholes, Heston, and Stein-Stein and more complex issues like path-dependent volatility models. We also dive into the pricing of Asian options, volatility, and variance swaps, bonds, and bond options. 

In addition to deriving novel solutions to classical problems, we have also applied our methods to the cutting-edge problem of hedging the risk of impermanent loss in smart contracts for trading cryptocurrencies known as Automated Market Makers (AMMs). Finally, we touch on the potential for further applications of Kelvin waves in financial engineering, showing how broad and flexible our approach can be.

The book by A. Lipton “Hydrodynamics of Markets: Hidden Links Between Physics and Finance” will be published by Cambridge University Press in the Spring of 2024 as part of Cambridge Elements Series.

It will be freely downloadable from their website.