Special Topics in Applied Mathematics

AMS-691.1

Spring 2009 Tentative Syllabus

Instructor: X. L. Li, Ph. D., Professor

Class information:W 6:50-9:40PM, Chemistry 124

Office: Math Tower 1-121

Office Phone: 632-8354

Home Page: www.ams.sunysb.edu/~linli

Email: linli@ams.sunysb.edu

Office Hours: 2:00pm-4:00pm MW or by appointment in Math 1-121

Text book: A Mathematical Introduction to Fluid Mechanics

Course Description:

  • Introduction to Brownian motion and stochastic process.
  • Ito's lemma and Black-Scholes equation.
  • Arbitrage and the limit of binary trading.
  • Analytical methods and similarity law.
  • Numerical methods for reaction, convection and diffussion equation.
  • Finite difference method for Black-Scholes equation, Crank-Nicolson scheme.
  • Time-dependent interest rate and volatility, contionous and discret dividends.
  • American option and free-boundary problem.
  • Future, forward contracts and other exotic options.
  • Convertible bond and multi-dimensional solutions.


    We recommend two reference books:
    (1). The Mathematics of Financial Derivatives, by Paul Wilmott et al, ISBN 0-521-49699-3.
    (2). Computational Methods for Option Pricing, by Yves Achdou and Olivier Pironneau, ISBN 978-0-898715-73-6.
    The course uses notes and the Wikipedia.

    Attendance: All students are expected to attend all classes and all exams.

    Grading: Course grade is determined by credit from assignments, midterm and final exam through the following table:

    Items Counted/Submitted Credit/Item Total Credit
    Assignment 3/3 100 300
    Final Exam 1/1 300 300

    Course Policy: Each assignment will be collected one week after it is distributed. Each sectional test will be 1 hour and 10 minutes. Final exams will be 2 hours and 20 minutes. Students are allowed to drop the grades of two assignments and one test. There will be no makeups on assignments, tests and final exams. Each test will be announced at least one week ahead. Final exam will be announced two weeks ahead.

    If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, I would urge that you contact the staff in the Disabled Student Services office (DSS), Room 133, Humanities, 632-6748v/TDD. DSS will review your concerns and determine with you what accommodations are necessary and appropriate. All information and documentation of disability are confidential.

    Important Note: Students are urged and encouraged to ask questions during and after the class. If you need help, please come to see me during office hours. If you cannot come during office hours, make an appointment and ask questions any other time. The University at Stony Brook expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws and University regulations; and to respect the rights, privileges, and property of other people. Faculty is required to report disruptive behavior that interrupts faculty’s ability to teach, the safety of the learning environment, and/or students’ ability to learn to Judicial Affairs.