642:621 Financial Mathematics: Home Page

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Class meets: TTH4 (1:40-3:00), Hill Center, Room 124
Text: Stephen E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer Verlag, 2004, ISBN 0-387-40101-8.
Instructor: Daniel Ocone, ocone@math.rutgers.edu
Office Hours: Hill 518: Tuesday, 11:00-12:20 and 6:20-7:20; Thursday, 3:30-4:30; and by appointment.
Lecture schedule, problem sets and reading assignments, etc. Click here.

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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.

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Prerequisites: The course will require a solid background in undergraduate analysis--calculus through differential equations (a course in methods of applied mathematics would also be helpful)--and a solid understanding of undergraduate probability at the level of the text, A First Course in Probability, by Sheldon Ross. Given this background, the course should be accessible to students in physics, engineering or economics.