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Dr. Kjell Konis
Acting Assistant Professor
Department of Applied Mathematics

About the Instructor

Professor Konis' research interests are in statistical computing. He is the author and maintainer of several packages for the R environment for statistical computing including robust (robust statistical models), lpSolveAPI (linear programming), and RHugin (Bayesian belief networks). Before joining the Applied Mathematics department, Kjell was a postdoctoral research associate in the Chair of Mathematical Statistics at the Swiss Federal Institute of Technology in Lausanne, Switzerland (Ecole Polytechnique Federale de Lausanne; where he conducted research in single particle electron microscopy, kernel smoothing, and forensic science.

About the Course

Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.

The Mathematical Methods for Quantitative Finance course reviews the mathematical methods fundamental for the study of quantitative and computational finance. The areas of focus include calculus and multivariable calculus, constrained and unconstrained optimization, and linear algebra.

Topics covered include the following:

• Functions and inverse functions
• Limits, derivatives, partial derivatives, and chain rule
• Integrals and multiple integrals, changing the order of differentiation and integration
• Taylor series approximations
• Newton's method
• Lagrange multiplier method
• Vector and matrix arithmetic, determinants, eigenvalue-eigenvector decomposition, singular value decomposition
• Numerical methods for optimization 

Course Goal

Upon completion of the course students will know the fundamental mathematical concepts needed to effectively study quantitative finance areas such as fixed income, options and derivatives, portfolio optimization, and quantitative risk management.

Learning Objectives

Upon completion of the course students will:

1. Understand the concept of a limit, differentiation, and integration;
2. Be able to compute partial derivatives and multiple integrals;
3. Understand the utility of matrix decompositions;
4. Be able to use Lagrange multipliers to solve constrained optimization problems; and
5. Apply the above methods to problems arising in finance.

Course Prerequisite

Students should have completed entry-level college calculus courses that include an introduction to multivariable differential calculus; additional introductory mathematics and statistics coursework is desirable.

Statement of completion or certificate issued for this course?

No, sorry there is not a credential awarded for this course.

Assessments and Activities

The class will consist of lecture videos, which are between 8 and 12 minutes in length and there is a short quiz at the end of each video. Additionally, there is a homework assignment accompanying each set of 8-10 videos

Discussion Forums

Discussion forums in Coursera are a great resource. They allow you to discuss the course with other students. Here, you may ask questions regarding the material or assignments, or respond to other students in need of help. You may also report technical issues, such as broken links, in the Technical Feedback Forum.

These open-ended questions may be designed to stimulate discussion and a variety of responses from many different perspectives. You are encouraged to actively participate in these discussions and to read and respond to other postings.

Please be courteous when posting. The University of Washington's Department of Professional and Continuing Education has created a set of guidelines for courteous and effective online posting, available at http://www.pce.uw.edu/resources/online/netiquette.html . You'll find other guidelines, with examples, at the top of the "Discussion Forums" page in this course.

Unfortunately, due to the large number of students enrolled in the course, Dr. Konis will not be able to respond directly to questions.

We look forward to providing you with additional courses from the University of Washington in the future.

Suggested Readings

Stefanica, D. (2011). A primer for the mathematics of financial engineering. (2nd ed.). New York, NY: Financial Engineering Press. Retrieved from http://www.fepress.org/primer-second-ed/

Thank you for your participation in this course.
- The University of Washington