IEOR E4007: Optimization Models and Methods for Financial Engineers

IEOR E4007: Optimization Models and Methods for Financial Engineers

COURSE BENEFITS

Learn to model optimization problems
Learn a portfolio of modern optimization techniques
Learn to apply the modeling methodology and optimization techniques to problems in finance.

PROFESSOR IYENGAR

Associate Professor, Department of Industrial Engineering and Operations Research
Research interests include:

Conic optimization problems: Linear programming, second-order cone problems and semidefinite problems
Integer and discrete optimization problems
Applied probability

APPLICABLE DEGREE PROGRAMS

Most courses 4000-level and above can be credited to all degree programs. All courses are subject to advisor approval.

ADDITIONAL COURSE FEES

None

Lecturer/Manager:

Lecturer: Garud Iyengar

Course Manager: Ali Sadighian

Office Hours:

The best method of contact is to reach the course manager via email.

E-mail Address:

Please contact the course manager, Ali Sadighian via email at: ali.sadighian@columbia.edu for questions related to this course.

Day & Time of Class:	Pre-taped course
Viewing Schedule:	Two lectures per week
Class Location:	All course lectures are available remotely via CVN
Class Homepage:	http://www.columbia.edu/~as2446/ta/4007/ (only accessible to registered students)
Credits for Course:	3
Class Type:	Lecture

Prerequisites:	Some exposure to linear algebra
Description:	This course is intended to introduce students, in particular the MS students in the financial engineering program, to an array of optimization techniques. This course should also be of interest to students from other departments that use mathematical programming and optimization techniques for analysis and design. The course will cover linear, quadratic, nonlinear, dynamic and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering will be discussed.
Required Text(s):	Applied Mathematical Programming /by Bradley Hax and Magnanti. This textbook will be available online.
Homework(s):
Project(s):	None
Paper(s):	None
Midterm Exam(s):	Yes - one Midterm
Final Exam:	Yes
Hardware Requirements:	PC with modem or telnet capabilities
Software Requirements:	Microsoft Excel, (Recommended but not needed Matlab - basic features no special toolbox needed)
Homework Submission:	Upload or Via fax to CVN at (212)-854-0466

Grading Scheme

Overview of Lectures

Session 1	Basic mathematics (Review of linear algebra, Review of calculus, Simple unconstrained optimization problems)
Session 2	Introduction to linear programming (Definition of linear programs Geometry of linear programs Rudimentary simplex algorithm Duality and shadow prices)
Session 3	Linear programming models (Blending model: oil arbitrage problem, Operations models: nurse scheduling problem, time-indexed models: short term financing problem, dedicated bond portfolio problem)
Session 4	Linear programming models (Linearizable models: hedging, No-arbitrage and martingale pricing)
Session 5	Nonlinear programming (Taxonomy of nonlinear programs, optimality conditions, quadratic programming)
Session 6	Quadratic programming
Session 7	General nonlinear programming (Markowitz portfolio selection, Capital asset pricing model)
Session 8	Integer Programming (Definition, Survey of integer programming models, Applications: fixed transaction cost, index fund construction, designing CMOs)
Session 9	Integer programming
Session 10	Dynamic programming models
Session 11	Dynamic programming

For more information, comments, or suggestions, please email us at cvn@cvn.columbia.edu.