16:642:621 Mathematical Finance I (Fall 2006)


Class Schedule: M7-8 (6:40PM-9:30PM), Hill 705 [first meeting Monday, September 11]

Textbook: Stephen E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer Verlag, 2004, ISBN 0-387-40101-8.

Note: The textbook may be purchased either new or used at significant discounts to the list price ($69.95) from online sellers such as Buy.com, and others found through Instructor: Paul Feehan (Hill 544, feehan at math.rutgers.edu, 732.445.5961)
Office Hours: Monday, 4:00-6:00PM and by appointment.

Teaching Assistant: Ming Shi (Hill 620, mingshi at math.rutgers.edu, 732.445.8211)
Office Hours: Tba and by appointment.

Course Website: Lecture schedule, problem sets, reading assignments, and related material (may be out of date and will be updated regularly).

Course description:
This course is an introduction to modern mathematical analysis of financial markets and financial instruments. The finance concepts, such as financial derivatives and no arbitrage, and the basic probabilistic ideas for their analysis will be introduced first and briefly for discrete time models. After this introduction, the course will move to continuous time models. It will cover Brownian motion, martingales, stochastic calculus, diffusions and their related partial differential equations, and apply these to modeling financial markets and to the valuation of derivatives. Major goals are the Black-Scholes option pricing formula, risk neutral pricing, hedging, and the study of American and exotic options.

Prerequisites:
The minimum prerequisites include one-semester undergraduate courses on probability theory, statistics, ordinary differential equations, partial differential equations or engineering mathematics, and linear algebra. A solid understanding of undergraduate probability at the level of the textbook by Sheldon Ross, A First Course in Probability, is especially important. Given this background, the course should be accessible to Mathematical Finance master's degree students and graduate students in Computer Science, Economics, Finance, Engineering, Mathematics, Physics, Operations Research, and Statistics.