January 11, 2010
26:960:580 Stochastic Processes
Ph.D. Program, Rutgers Business School

Time: Tuesdays, 9:00-11:50 am.
Methods in Supply Chain Management,
which is also offered this semester (M
5:30-8:20, Michael Katehakis).
Spring 2010
My own research bases probability
theory on games instead of measures:
www.probabilityandfinance.com.
Place: Room 532, 1 Washington Park, Newark
Instructor: Glenn Shafer, Room 936
 973-353-1604, fax 1283,
 gshafer@rbsmail.rutgers.edu.
Tentative Schedule
1. January 19. Lecture 1. Ch. 1.
Introduction.
2.
January 26. Lecture 2. Ch. 2, §§1-3.
Probability in discrete time.
3.
February 2. Lecture 3. Ch. 2, §§1-3.
Martingales & central limit theorem.
4.
February 9. Lecture 4. Ch. 3, §§1-2.
Defining Brownian motion.
5.
February 16. Lecture 5. Ch. 3, §§3-4.
Tricks & theorems.
6.
February 23. Lecture 6: Ch. 4, §§1-2.
Stochastic integration.
7.
March 2. Lecture 7: Ch. 4, §3.
Ito’s formula.
8.
March 9. Lecture 8: Ch. 4, §4.
Integration by parts.
9.
March 16. No class. Spring break.
Office hours: Tuesdays, 3:30-4:30 and
thereafter as necessary.
People who sometimes know where I am:
 Jackie Adams 973-353-1644,
Accounting, Room 912
 Monnique DeSilva 973-353-5371,
Ph.D. Program, 403C
Course Resources:
 A course in financial calculus, by
Alison Etheridge. Cambridge, 2002.
The Rutgers-Newark Bookstore and
New Jersey Books both have copies of
the book.
 Slides posted on Blackboard each
Monday evening before Tuesday class.
Other Books:
 Less mathematical: Martin Baxter and
Andrew Rennie, Financial Calculus.
 More mathematical: Steven E. Shreve:
Stochastic Calculus for Finance II.
Coursework and grading:
 Homework, always due at the beginning
of the next class: 30%
 One-hour exam March 23: 30%
 Final exam: 40 %
Any needed make-up exam will be oral.
Some aspects of the philosophy of the course:
 The course will be about Brownian
motion and Ito processes. Within
business schools, these models are
applied mainly to finance, but they have
many other applications in science and
mathematics.
 Discrete-time stochastic processes such
as Markov chains and counting
processes such as the Poisson process,
are covered in 26:799:661, Stochastic
10. March 23. Lecture 9: Ch. 4, §5.
Girsanov’s theorem
11. March 30. Midterm examination.
12. April 6. Lecture 10: Ch. 5, §8.
Feynman-Kac
13. April 13. Lecture 11: Ch 5, §1-2.
Black-Scholes
14. April 20. Lecture 12: Ch 5, §3-6.
Foreign exchange, etc.
15. April 27. Lecture 13: Ch. 6.
Other payoffs
16. May 11. Final examination.