|Math 408 Section A
||Mon. 11:30-12:20 and
Fri. 11:30- 12:20
||& by appointment|
||Math 327 and 308 (or 318)
URL for the course website:
David Luenberger, Investment Science
A mathematical optimization problem is one in which a given function is either
minimized or maximized relative to some set or range of choices available
in a given situation.
Optimization problems arise in a multitude of ways as a means of
solving problems in engineering
design, portfolio design, system management, parameter estimation,
and in the modeling of physical
Math 408 is an introductory course in numerical methods for
continuous optimization in finite dimensions. This term
the course is being taught
with an emphasis on applications in financial optimization.
We will learn how the techniques of optimization modeling
and numerical solution methodology can be applied to a range of
important problems in finance.
The financial models we consider include linear portfolio optimization,
the mean-variance portfolio theory of Markowitz,
the capital asset pricing model,
value-at-risk, expected value at risk, and the construction of indexed funds.
The optimization tools that we consider cover much of what is known as
mathematical programming. We begin with linear programming and then
progress through quadratic programming to nonlinear programming and
integer programming. Special emphasis is given to the duality theory and
Background and Prerequisites:
This course requires a background in multi-variable calculus. In order
to succeed you will need to be conversant with the differential
properties of smooth vector valued mappings
In particular, you will need to know properties of the gradient
and Hessian. Moreover, some background in linear algebra is
also required. In particular, you will need to know some results
concerning the eigenvalue decomposition of a symmetric matrix,
Gaussian elimination (LU
factorization), and Gram--Schmidt orthogonalization (QR
factorization). However, I do not expect everyone to have the
the same level of preparation. Consequently, all of the material
discussed above will be reviewed with most proofs omitted.
There are 9 fifteen
minute quizzes each worth 50 points. The
quizzes are given each Friday except February 13. The
quizzes cover the homework of the previous week. The potential content of
the quiz will be announced the Wednesday before the quiz.
The top 7 of your
quiz scores count toward your grade.
Three take-home assignments will be given each worth 50 points.
These are extended homeworks
that will require the use of a range of skills. You will be asked to
model a financial optimization problem, solve the problem using
a computer package, and then write a report on the model and its
There is one midterm: Friday, February 13. The
content of the midterm will be discussed in advance and a sample midterm
will be distributed before the exam. The midterm is worth 200 points.
The final exam is to be given on Monday, March 15
from 8:30 to 10:20 am. The final exam is comprehensive. A sample final exam
will be distributed. The final exam is worth 300 points.
Final Grade: The total number of possible points is 1000:
Your final grade will be based on these points.
One class curve is computed
after the final exam has been scored.
Your final grade will be computed as the maximum of the class
curve grade and one grade point below your final exam grade.
Therefore, your final grade can be no lower than one grade
point below your final exam grade.
|350 quiz pts 150 assignment pts
200 midterm pts 300 final
exam pts 1000 points.
Time Conflicts with an Exam:
There will be no make-up exams except
in the case of a documented emergency.
In the event of an unavoidable conflict with a midterm
(an athletic meet,
wedding, funeral, etc...), you must notify me as soon as you are
aware of the conflict (a minimum of 1 week prior to the exam date)
so that we can arrange for you to take the exam BEFORE the
actual exam date. In the event of an unavoidable conflict with the final
exam, you will need to submit a written petition for this purpose to me
March 5, or as soon as you are aware of the conflict.
No make-up quizzes will be given since your lowest two quiz scores
will be dropped.
A grade of Incomplete will be given only
if a student is doing satisfactory
work up until the end of the quarter, and then misses the final exam due to
a documented medical or family emergency.
OFFICE HOUR RULES
If no student arrives within the first 15 minutes
of office hours, then I will assume that no student will be coming
for office hours that day unless other arrnagements have been made.
In this case, I will attend to my other University duties, and so
I may leave my office at that time.
However, it is important to remember that you
are always free to make an appointment to see me
at a time other
than the scheduled office hours. You can arrange such an appointment by
either speaking directly with me in person, by phone, or by
Holidays: January 19, Martin Luther King Day:
February 16, Presidents Day.
Quiz Dates: Jan. 9,16,23,30: Feb. 6,20,27:
Midterm Date: Friday, February 13.
Final Exam: Monday, March 15, 8:30-10:20 am.