** Professor Williams' Office hours for Finals Week only:
Monday, March 19, 3-4 p.m.,
Wednesday, March 21, 2-3 p.m. **

**
Final Exam: Thursday, March 22, 2001, 3-6 p.m., PETERSON HALL 103
(NOTE LOCATION IS NOT THE USUAL CLASS ROOM) **

** Section Time: ** Tu 4.40-5.30 p.m. ** Section Place: ** York 4050A.

** Teaching Assistant: ** Tucker McElroy, Office: AP&M 2325, email: tmcelroy@math.ucsd.edu

** TA Office Hours: **
Monday, 10 a.m.-noon.

**
DESCRIPTION: **
This course is an introduction to the mathematics of
financial models.
The aim is to provide students with an introduction to some basic
probabilistic models of finance and associated mathematical machinery.
The emphasis will be on discrete time models where concepts
can be developed without measure theory.
(The graduate course, Math 294, which has a similar
title, is at a more advanced level and has much more emphasis on continuous
time models which use measure theory.)

** PREREQUISITES: ** Math 20D, Math 20F, and Math 180A or Math 183.

** TEXT: **
S. Pliska, Introduction to Mathematical Finance: Discrete Time Models,
Blackwell, third printing, 1999.
This text will be used as a primary reference for the
course.
The lectures will provide a guide and expanded explanation of the
relevant topics.

** OUTLINE **
The course will roughly follow a selection of topics from the text "Introduction to Mathematical Finance -- discrete time
models" by S. Pliska. The treatment of that book will be supplemented with mathematical background and details as needed. In
particular, conditional expectation, martingales and optimal stopping will be
discussed.
The
course will begin with the development of the basic ideas of hedging and
pricing by arbitrage
for single period models and then multiperiod securities market models.
These ideas will be adapted and applied to price various derivative securities including European and
American options.
The fundamental theorem of asset pricing will
be covered.
An important example throughout will be the
binomial tree model. As time allows, additional topics
will be covered.

** OTHER REFERENCES: **

J. Hull, Options, Futures and other Derivative Securities, Prentice Hall,
Fourth Edition, 2000.

S. Ross, An Introduction to Mathematical Finance, Options and other topics,
Cambridge University Press, 1999.

J. Stampfli and V. Goodman, The Mathematics of Finance: Modeling and
Hedging, Brooks/Cole, Pacific Grove, CA, 2001.

P. Wilmott et al., The Mathematics of Financial Derivatives,
Cambridge University Press, 1995.

** OTHER COURSES: ** Math 168A, Statistical and
Optimization Methods in Finance, will be offered in Spring 2001 by Professor
Hans Sieburg. This course is designed to follow on from Math 194 and will be an excellent practical complement to the material
learned in Math 194. Click
here to see a description of the course.
Please direct any questions concerning this course
to Professor Sieburg, hsieburg@ucsd.edu.

** LINKS TO RELATED WEB SITES (under construction):
**

** HOMEWORK: For the homework, click here. **

Please direct any questions to Professor Ruth J. Williams, email: williams@math.ucsd.edu