The
objective of this course is to introduce models and computational methods for static
and dynamic optimization problems occurring in finance. Special attention will
be devoted to portfolio optimization and to risk management problems.
Prerequisites: Operations Management, Statistics.
Tuesday
2:30—5:20, 1WP-464 (Newark Campus)
Wednesday
2:00—
Lecture Notes.
D.G. Luenberger,
Investment Science,
Oxford University Press, New York 1998
A. Ruszczynski, Nonlinear Optimization, Princeton University Press,
2006.
The books are not required, but
you may consult them if you want to deepen your knowledge in some areas.
Homework
will be assigned twice a month as a means to help you understand the concepts
and to give you practice in applying them. There will also be a final project.
Homework assignments and other information can be obtained from the course web
page.
Week
|
Topic
|
1
|
Linear programming models. Optimality.
|
2
|
Duality in linear programming. Application to asset pricing.
|
3
|
Nonlinear programming models. Optimality.
|
4
|
Duality in nonlinear programming. Economic interpretation of Lagrange multipliers.
|
5
|
Expected utility optimization.
|
6
|
The portfolio selection problem. The concept of risk.
|
7
|
Two-fund and one-fund theorems.
|
8
|
Value at risk. Conditional value at
risk.
|
9
|
General theory of mean-risk optimization models.
|
10
|
Coherent measures
of risk. Duality.
|
11
|
Optimization of coherent measures of risk.
|
12
|
Stochastic dominance. Relations to utility theory and measures of risk.
|
13
|
Two-stage stochastic optimization models.
|
14
|
Multistage stochastic optimization models.
|
Handouts and Homework are
available on Blackboard.