168a: "Statistical and Optimization Methods in
Instructor: Hans B. Sieburg
Term: Spring 2000-01
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.
"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.
The main course text will be
Simon Benninga, Financial Modeling. 2nd edition. MIT Press, Cambridge,
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,
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.