IEOR E4602: Quantitative Risk Management (Columbia University, Spring 2016)

I last taught this advanced-level MS course in fall 2016 in the IE&OR Department at Columbia University. It is an elective course for the MS in Financial Engineering and MS in Operations Research programs at Columbia.I will not be posting solutions to the assignments or code / software so please donít send me an email asking me to do so!Finally, please note that I do not have time to answer emails asking me to clarify or explain issues arising in these notes and assignments. A syllabus and description of the course logistics can be found here.


Lecture Notes

  1. Basic Concepts & Techniques of Risk Management and slides
  2. Multivariate Distributions and slides
  3. Dimension Reduction Techniques and slides
  4. An Introduction to Copulas and slides
  5. Risk Measures, Risk Aggregation and Capital Allocation and slides
  6. Model Risk and slides (The maths behind the some of the derivatives models in these notes is somewhat advanced. Students were not expected to know this.)
  7. Asset Allocation and Risk Management and slides
  8. Monte-Carlo Methods for Risk Management and slides
  9. Extreme Value Theory (The course never made it this far in 2016)

10.  Risk Management & Time Series (Nor did the course get this far in 2016)


A brief review of some derivatives pricing theory can be found here. It might be of some use for some parts of the course.



  1. Assignment 1 and spreadsheet and explanatory file
  2. Assignment 2 and spreadsheet
  3. Assignment 3 and spreadsheet and Matlab file
  4. Assignment 4
  5. Assignment 5
  6. Assignment 6
  7. Assignment 7
  8. Assignment 8 (From the 2015 version of the course when some of the earlier topics werenít covered in as much detail as they were in 2016)