Section Time: Tu 4.40-5.30 p.m. Section Place: York 4050A.
Please note that the first section will meet on January 16, 2001, at 4.40 p.m. in the INTEL lab located in the basement of AP&M (room B349).
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, Introduction to Numerical 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 and click here to see the course home page (these descriptions are from last year, but will give you an idea of what is planned for the course).

LINKS TO RELATED WEB SITES (under construction):

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