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# York University

## GS/MATH 6910.03AF, Fall 1999

# STOCHASTIC CALCULUS IN FINANCE

Course Outline

### Prerequisites:

Calculus and some basic probability. In particular, Measure Theory is not
assumed. This course is designed (and required) for the
Diploma in Financial
Engineering,
which can be pursued in conjunction with either an
M.A. or an
M.B.A..
Other students are also welcome in the course.
### Degree credit exclusions:

None. In particular, though there may be some overlap
with the Measure Theory and Stochastic Processes courses
(see MATH6280.03 and MATH6602.03 in the
grad calendar),
mathematics or statistics students are encouraged to take the latter as
well.
### Instructor:

Tom Salisbury
- email: salt@yorku.ca
- Office: N625 Ross Building
- Phone: (416) 736-5250 (via Math Dept.)

(416) 736-2100 extension 33938 (via York switchboard)
- Fax: (416) 736-5757

### Lectures:

S173 Ross, Wednesdays and Fridays, 10:00 - 11:30
### Office hours:

Monday 10:30-11:20, Friday 12:30-1:20.

If you need to see me outside these hours, you are welcome to drop by my
office. If I am able to talk to you then, I will; if not we can arrange
another time. Or you can e-mail to arrange an appointment.
### Grading:

- 30% Assignments (three or four)
- 30% Project
- 40% Final exam (take-home)

The project will be on a topic you select and clear with me, that must involve
stochastic calculus in some way (applying it, explaining some results or
ideas, etc.). You'll write it up and give a 20 minute presentation to the
class summarizing what you did.
### Text:

*Stochastic Differential Equations*
by Oksendal; 5th edition, Springer Verlag 1998.

This book has been ordered, and is available at the bookstore. I'll refer to
it frequently. It is a textbook level introduction to stochastic calculus.
### Other references:

*Financial Calculus* by Baxter and Rennie; Cambridge 1996.

This book is also at an introductory level, and
focuses more on finance than Oksendal, but does much less stochastic
calculus. It has the best textbook level introduction I have seen to the
ideas of risk-neutral pricing.
*Introduction to Stochastic Integration* by Chung and Williams, 2nd
edition, Birkhauser 1990.

A nice textbook level introduction to stochastic calculus.
More theory than Oksendal but fewer applications.
- Reference books for stochastic calculus, doing much more than we'll have
time for:
*Brownian Motion and Stochastic Calculus*
by Karatzas and Shreve, Springer.
*Continuous Martingales and Brownian Motion* by Revuz and Yor,
Springer.
*Diffusions, Markov Processes, and Martingales, Vol 1,2*
by Rogers and Williams, Wiley.