Non-classical arithmetics replace ordinary addition and/or multiplication in standard arithmetic with other binary operations called pseudo-addition and multiplication. Dynamic non-classical arithmetic (DNA) allows a different non-classical arithmetic to be used at each time. We apply DNA to enhance our understanding of the logistic distribution in probability theory. We also apply DNA to develop a novel arbitrage-free option pricing model in finance. Under our approach, European option valuation reduces to pseudo-addition of spot and strike, while Bermudan option valuation reduces to repeated pseudo-addition. Simple and realistic closed-form formulas are easily generated in both cases.

We are going to discuss the celebrated Falconer distance conjecture, which asks for the smallest possible Hausdorff dimension of a compact subset of Euclidean space that guarantees that the set of the pairwise distances between the points in the set has positive Lebesgue measure. The study of this problem has led to the development of a wide variety of techniques from different areas of mathematics. We shall discuss these ideas and some of the recent results in this subject area.

Abstract: In this talk I will give a brief overview of current academic research on Fintech by using tools from mathematics and statistics. The topics to be discussed include: (1) Designing stable coins: how to design stable cryptocurrency by using option pricing theory. (2) P2P equity financing: how to design contracts suitable for a P2P equity financing platform with information asymmetry. (3) Econometrics with privacy preservation: how to do econometrics based on the encrypted data while still preserving privacy. (4) The wisdom of the crowd and prediction markets: how to use the collective opinion of a group to make predictions. All the above 4 topics are based on my recent papers.



Bio: Steven Kou is a Questrom Professor in Management and Professor of Finance at Boston University. Previously, he taught at National University of Singapore (from 2013 to 2018), Columbia University (from 1998 to 2014), University of Michigan (1996-1998), and Rutgers University (1995-1996). He teaches courses on FinTech and quantitative finance. Currently he is a co-area-editor for Operations Research and a co-editor for Digital Finance, and has served on editorial boards of many journals, such as Management Science, Mathematics of Operations Research, and Mathematical Finance. He is a fellow of the Institute of Mathematical Statistics and won the Erlang Prize from INFORMS in 2002. Some of his research results have been incorporated into standard MBA textbooks and have implemented in commercial software packages and terminals, e.g. in Bloomberg Terminals.