** Professor: **
Professor R. J. Williams, AP&M 7161.

** Class Time: ** Tu Th, 5-6.30pm. (There will be no class on Thu Jan 11 nor Thu Feb 22. This class time is being made up with longer class time for other days.)

** Class Meeting Place: ** AP&M 5402.

** Professor Office Hours: ** AP&M 7161, Tuesday noon-12.50pm, Thursday 11am-11.45am, and by appointment. No office hours Feb 6, 8, 22.

**
DESCRIPTION: **
This course is an introduction to the mathematics of financial models at the
graduate level.
The aim is to provide students with an introduction to some basic
models of finance and the associated mathematical machinery.

** OUTLINE: **
The course will begin with the development of the basic ideas of hedging and
pricing by arbitrage
in the discrete time setting of binomial tree models.
Key probabilistic concepts of conditional
expectation, martingale, change of measure, and representation,
will all be introduced first in this
simple framework as a bridge to the continuous model setting.
Mathematical fundamentals for the development and analysis of continous time
models will be covered, including Brownian motion, stochastic calculus, change
of measure, martingale representation theorem. These will then be combined
to develop the Black-Scholes option pricing formula.
Pricing and hedging for European and American call
options may be discussed.
As time allows, additional topics will be discussed, possibly
including models of the interest rate market.

** TEXT: **
Introduction to the Mathematics of Finance, R. J. Williams,
American Mathematical Society, 2006.
AMS members receive a discount if they buy the book directly
from the AMS.

** PREREQUISITES: ** A course in probability or consent of instructor.
A possible probability course is Math 280AB (Graduate Probability).
However, other probability courses may be used in place of this with the
consent of the instructor. Some knowledge of conditional
expectation and martingales is an asset.
For background reading, students may wish to look at
the books below by Billingsley or Chung.
The course
Math 286 (Stochastic Differential Equations) is a very useful
complement to Math 294 and students may find it helpful to take Math 286
before or after Math 294.

** HOMEWORK: Click here for homework. **

** INTERESTING WEB LINKS: **

** REFERENCES: **

* Background in Probability and Stochastic Calculus: *

Please direct any questions to Professor R. J. Williams, email: williams at math dot ucsd dot edu

Last updated November 5, 2017.