MATH 168a:  "Statistical and Optimization Methods in Finance"

Instructor: Hans B. Sieburg

Term: Spring 2000-01

Course Description:

This course is mainly thought for mathematics, economics, and international studies students with an interest and/or specialization in finance. Its focus is on numerical methods related to the statistical and optimization theory of finance. Therefore, purely mathematical theory will organically interface with algorithmic and computational approaches. Added features include the use of neural nets, and so-called "information discrimination" measures. To obtain a feel for which theories and techniques associate with which problems in finance, and how solutions are to be interpreted, we will present a number of case studies in money management, corporate finance, and risk management. A portfolio competition among participant groups will supply additional practical experience.

We will initially provide a brief and self-contained introduction to the terms and problems in finance that are relevant to this course in order to achieve a common denominator of terms. This section will also formulate the fundamental case studies. Next, after explaining the basics of mathematical programming and how to interpret statistical problems in this framework, we shall recast the fundamental case studies in terms of optimization problems. The third main section of the course focuses on solving these optimization problems numerically. This will involve spending lecture time in a computer lab.

Requirements:

"Statistical and Optimization Methods in Finance" is conceptualized at the advanced undergraduate level, i.e. for participants who have knowledge of essential calculus and linear algebra, and who have the ability to perform spreadsheet calculations. Knowledge of Mathematica and/or MatLab would be convenient, but is not a necessary pre-requisite.

Literature:
The main course text will be

Simon Benninga, Financial Modeling. 2nd edition. MIT Press, Cambridge, Massachusetts, 2000.

This text shall be complemented with the instructor's course notes and a number of milestone papers taken from the recent literature in computational finance. We also recommend

"Numerical Linear Algebra and Optimization" by Ph. Gill, W. Murray, and M. Wright. Addison Wesley, Redwood City 1991.

Raul Rojas, Neural Networks - A Systematic Introduction. Springer, Berlin 1996.

T. S. Arthanari, and Yadolah Dodge, Mathematical Programming in Statistics. Wiley Series in Probability and Mathematical Statistics. Wiley, New York, 1981.

Peter L. Bernstein, Against The Gods - The remarkable story of risk. Wiley, New York 1998.