Math 194, Mathematics of Finance
Spring 2004

Instructor: Michael Sharpe, 7121 AP& M: msharpe@ucsd.edu

Office hours MWF 11:00 to 11:30 and 1:00 to 1:30, or by appointment

TA : Lei Wu, 2250 AP& M: lwu@math.ucsd.edu

Office hours: 3:45--5:00 Tuesdays.

Course text: There is no required text. I plan to use the first 3 chapters of the lecture notes of Professor Ruth Williams, which may be downloaded from http://www.math.ucsd.edu/~williams/courses/past/m294notes-w03/math294notes03.html The notes are intended for a graduate course, but the first 3 chapters may be understood by undergraduates. I shall fill in the details and background needed. Those wishing more detail might wish to consult the book Introduction to Mathematical Finance: Discrete Time Models, by Stanley Pliska (Blackwell Publishers.) While I can't recommend this as a suitable text for the course, it does have some topics that I shall borrow as introductory material and background, and I shall place the book on soft reserve.

Course description: This course is an introduction to the mathematics underlying financial modelling, with emphasis on discrete models. As background, I shall have to develop the appropriate tools from linear algebra and probability theory. In particular, the notions of filtration, conditional expectation and martingale will be derived from basic knowledge of probability theory at the level of Math 180A or equivalent. The Black-Scholes formula will be derived as a limit from the binomial model. No previous knowledge of financial mathematics is assumed.