Professor Philip Protter of the Departments of Mathematics and Statistics has received a three-year grant from the National Science Foundation to organize meetings of French and American researchers. The NSF program, intended to foster international exchange, is part of a cooperative agreement with the INRIA (Institute Nationale de Recherche en Informatique et Automatique), a French governmental institution dedicated to supporting research in Computer Science and Applied Mathematics and to helping French industry.
Five French researchers and ten Americans attended the first meeting, hosted by Purdue, in March 1995. The meeting's topic was "Stochastic Numerics," a relatively new subject which is currently more advanced in France than in the U.S. The idea is that one can use stochastic differential equations to model dynamical systems that are subject to corruption by noise. One can gain tremendous understanding of how the system works this way, but to put things to practical use, one often has to solve the equations numerically, with the aid of a computer. Since the systems involve randomness, computer simulation of random variables is also needed.
Such issues have long been studied by electrical engineers in Statistical Communication Theory. A new and exciting application is Finance Theory in economics, more specifically, options trading. Here one has a mathematical model, the Black-Scholes Formula, that works in the sense that it gives a fair price to an option. The model has some rather strong assumptions, and much attention has been devoted to getting better models and extending these ideas to analyze more complicated situations, such as currency fluctuations. The numerical techniques needed present interesting mathematical challenges.
Protter is organizing the second meeting, to be held at INRIA in France in the spring of 1996. A third meeting, probably at Purdue, is envisioned for 1997.