Ever since high school, when I attended the Hampshire College Summer Studies in Mathematics, I planned a career in mathematics.
At first my career took a traditional academic route, I earned a Bachelors of Science Degree in Mathematics from Caltech. Professor Richard Wilson introduced me to discrete mathematics which would eventually become my thesis topic at MIT. Meanwhile I added breadth to my mathematical training by taking a number of computer science and economics classes. Caltech studies microeconomics and game theory from a very mathematical approach. In fact I often found the mathematics in my economics courses more challenging than the mathematics in my math courses: maximizing a function of a dozen variables with several constraints, whereas in math after getting past explicit examples in 2 or 3 variables we always went straight to the "general case".
At MIT, I studied umbral calculus (a branch of combinatorics) under the direction of Prof. Gian-Carlo Rota and received my Ph.D. in 1989. I then taught and continued my research at the University of Bordeaux in France.
In 1996, I was looking to take a sabbatical and return for a while to the United States. A coauthor of mine Walter Stromquist encouraged me to consider non-academic employment, so I applied to Daniel H. Wagner Associates where he was in charge of their Pennsylvnia office.
My first projects at Wagner Associates were redesigned the corporate website (which was a great initial project since it exposed me to the wide variety of mathematical work done at the fine) and to the evaluation of a credit risk model used by BMW based on fuzzy logic.
However, I soon started working in mathematical finance for the Susquehanna International Group for their newly created Statistical Arbitrage Group in their Quantitative Research Department. As this project continued to be successful and grew in size, it took up all of my time and I eventually left Wagner Associates to work fulltime at Susquehanna where I am now responsible for a group of over a half-dozen mathematicians developing proprietary trading strategies with which to invest to the partner's money.
Having worked in both industry and academy, I appreciate the comeradery of working within a groups of mathematical cohorts you find at Susquehanna similar to that at most universities. We share the same mathematical sence of humor and enjoy puzzles.
Outside of Quantitative Research, there are many traders who have ideas for us to try and who would like to exploit our models. However, traders will typically give a few examples rather than express their idea as a mathematical equation to be tested. Part of the excitement of my work is translating the ideas of the traders into mathematical formulae, and conversely helping the traders better understand and visualize the mathematical concepts behind our trading models.
In academia I spent most of my time working on publications. In many cases years would pass between writing up the idea and actually seeing it in print. At that point, I felt I was wasting my time in P.R. encouraging people to read my specialized work. For example the paper I am perhaps proudest of (Invariant Umbral Calculus) requires a strong background in combinatorics, Hilbert spaces, umbral calculus and physics, so it is not surprising that articles like that get limitted readership.
On the other hand at Susquehanna almost all of our work is confidential so I do not publish anything except in my spare time. However, my work is exciting, and if I find something useful I know it will get applied quickly. In some cases, it was literally minutes between coming up with an idea, implementing it in one of our computer based strategies, and actually trading it on the New York Stock Exchange.