**
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. *

** 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.

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

** OUTLINE: **
The course will roughly follow the topics covered in 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, change of measure, martingale representation
and optimal stopping will be
discussed and relevant topics from optimization theory
such as the separating hyperplane theorem and linear programming
will be included.
In addition, some structured computer modules
to illustrate the theoretical material will accompany the course.
The course will begin with the development of the basic ideas of hedging
and pricing by arbitrage, and consumption and investment theory, for
single period models and then multiperiod securities market models.
An important example throughout will be the
binomial tree model.
These ideas will then be adapted and applied to price various derivative
securities
including European and American options, and to solve
consumption investment problems.
If time allows, attention will then turn to models of the interest rate market
and treatment of interest rate derivatives such as caps and swaptions.

** COMPUTER MODULES: **
These will be made available to students
and will complement the theoretical material presented in the course.

A simple mathematica notebook showing how to do reduced row echelon
can be obtained by clicking here.

** READING: ** * IT IS VERY IMPORTANT THAT STUDENTS READ THE ASSIGNED
MATERIAL IN ADVANCE OF THE LECTURE. *
This will be expected and it will enable students
to maximize what they get out of lectures.

** HOMEWORK: ** For homework assignments, click here.
Homework is an essential part of the course.
To assimilate the theoretical material presented in lectures,
it is necessary to
solve problems such as those presented in the homework.
* IT IS OF GREAT IMPORTANCE THAT STUDENTS MAKE EVERY EFFORT
TO
COMPLETE EVERY
HOMEWORK ASSIGNMENT, AND THAT STUDENTS SEEK HELP
WITH
PROBLEMS THEY HAVE
NOT BEEN ABLE TO HANDLE. *
Homework
will count for 25% of a student's grade.
Homework assignments will be given out each week in class.
They will be due in section on Tuesdays.
* Late homework will not be accepted. *

** EXAMINATIONS: **
There will be * one * exam in class during the quarter
plus a * final * exam. The in class exam will count for 25% of a student's grade
and the final exam for 50%. Make-up exams will not be given.
For information concerning the exams, click here. In
particular, the midterm and final are in different rooms from the class room.

** EXAMINATION DATES: **

* In class exam: *
Wednesday, February 16, 2000.
* Final exam: * 3--6 p.m. on Saturday, March 25, 2000, WLH 2204.
The alternative final exam date is Wednesday, March 22, 1-4 p.m., Center Hall 205. Click here for more information.

** FINAL COURSE GRADE: **
For
the final grade, the homework will count
25%, the in-class exam 25%, and the final exam 50%.

** OTHER COURSES: **
Math 168A, Introduction to Numerical Methods in Finance,
will be offered in Spring 2000 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 and
click here to see the
current course home page.

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

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