# Math 6050                         Optimization                      Spring 2019

Instructor: Professor Jim Zhu
Office: 5516 EV, Tel: 387-4535, e-mail: zhu@wmich.edu
Web: http://homepages.wmich.edu/~zhu/
Office Hours: T. R. 1:50-2:40pm. Office:  EV5516
Class Hours:  T. R. 12:30-1:45pm Rood Hall 03307
Text:  Convex Duality and Financial Mathematics by P. Carr and Q.J. Zhu, Springer, New York, N. Y. 2018.

Course Description:

This is a topic course covering selected optimization methods and their applications. Topics are decided by the instructors and may change from year to year. This year we will focus on Convex Duality and its applications to financial problems. We start with a discussion on convex optimmization and duality.  We then turn to applications in finance.  First we establish the simple one period financial market model. Using this model we can discuss the typical problems involved in the financial markets. We then progress to multi-pereiod models for trading strategies and continuous model if time permits. This course often attracts students from different disciplines. Students are encouraged to participate in class discussions and to contribute ideas from their disciplines.

Prerequisites:

MATH 2720 and 4080 or 6080 or IEGM 6100 or other courses approved by the instructor.

Objectives:

We will start from convex optimization and duality. We emphasize the link between dual solution and the Lagrange multipliers. We will take a variational approach and emphasize the practical meaning  for the Lagrange multipliers.

Next we turn to applications in financial models. Since maximize concave utility and minimize convex risk is often the primary concern these financial problems are often convex. Making the convex duality theory particularly suitable tools.  It is often worthy noting the financial meaning of the Larange multipliers in these applications.

We will start with the simple model of portafolio theory in a finite economy and discuss various issues of importance to the financial community. We then generalize to trading theory that involves a multi-period economy.

Finally, we explore continuous financial models if time permits.

Academic Integrity: Students are responsible for making themselve aware of and understanding the policies and procedures in the Undergraduate (pp. 274-276) [Graduate (pp.25-27)] Catalog that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Homework 55%, midterm 10%, class participations 10%, and the final 25%. The final exam will be 2:45-4:45pm on Wednesday, April 24.

Grading scale is approximately as follows:

A (85-100%) BA(78-84.99%) B (71-77.99%) CB(60-70.99%) and C below 60%.

Homeworks:

Sections 1.1

Sections 1.2

Sections 1.2.3-4

Sections 1.3

Sections 1.4

Sections 1.4.3

Sections 2.1.1

Sections 2.1.2

Sections 2.2.1

Sections 2.3

Sections 2.4