The Program on Financial Mathematics at the University of Chicago is now (1998-99) in its third year of operation. This program was founded to meet the need of students for a rapid and in-depth introduction to the mathematics necessary for modern financial modeling. It results in award of the degree of Master of Science in Financial Mathematics.
The program has three three-quarter course sequences: Mathematics, Stochastic Calculus, and Financial Applications. A full-time student takes all three courses at the same time, to finish in 1 year. A part-time student can take either one or two courses per year, to finish in 2 or 3 years; if not taken concurrently, the courses must be taken in the above sequence. All these courses have been designed specifically for the Financial Mathematics program; they are open only to our students, with only a very few students from other programs permitted on a case-by-case basis. Our academic year begins in September with a 1-month sequence on linear algebra, basic numerical analysis, and computer programming, and continues through Chicago's regular academic year, finishing in mid-June.
The mathematics sequence is focused on partial differential equations and numerical methods for their solution: Brownian motion processes and the Black-Scholes diffusion equation, and the limitations of these models; binomial trees; explicit and implicit finite-difference methods; the free boundary problem for American options, and methods of approximate and numerical solution. We then cover Monte Carlo methods and numerical optimization; finally, neural network methods and nonlinear time-series analysis. This sequence is taught by Robert Almgren and Jack Cowan of the Department of Mathematics.
The stochastics sequence is a two-quarter treatment of the mathematics of continuous-time stochastic processes as they are relevant to the pricing and hedging of options and other derivative securities; the level is that of a graduate course in mathematics or statistics, making heavy use of measure theory. It is taught by Per Mykland of the Department of Statistics. The third quarter of this sequence is Economics, using the mathematics developed in the first two quarters.
Financial Applications is a series of six half-quarter courses, taught by professionals from the Chicago-area financial industry, many of whom have Ph.D.s in mathematics or related fields. It shows students how the models studied in the other courses are used in practice. The six components are Portfolio Theory and Risk Management I and II, Fixed Income I and II, Foreign Exchange, and Exotic Options.
By design, our program goes intensely into mathematical theory, with less emphasis on technical details such as use of specific software packages. Successful applicants must have a very solid undergraduate background in mathematics, including at least real analysis, linear algebra, and ordinary differential equations (some exposure to partial differential equations is very desirable).
It is a professional master's program, intended to prepare students to get jobs; it is not meant to be a preparation for further graduate study. To this end, it is very advantageous to have some work experience in the financial industry; previous exposure to basic economics and statistics, as well as computer programming skills, are also very useful. Some graduates have gone to the few major Wall Street firms; others find work in a wide variety of asset management and trading firms, and some in newer areas such as energy derivatives.
More information is at http://finmath.uchicago.edu