2025 Instructor
強健與隨機投資組合優化 Robust and Stochastic Portfolio Optimization (QF 527200)
Course Description & Audience: The course concentrates on studying several problems in robust and stochastic portfolio optimization. We aim to make optimal portfolio management robust with respect to various modeling risks. Coverage of material will be suitable for graduate students interested in quantitative finance, stochastic optimization, and theoretical portfolio management. The intended topics of the course are listed as follows.
Part 1: Review of Convex Optimization
Convex Sets
Convex Functions
Convex Optimization Problems
Optimization Under Uncertainty
Part 2: Robust and Stochastic Portfolio Optimization
Sensitivity of Mean-Variance Model & Factor Model
Black-Litterman Model
Unconstrained Optimization Theory
Duality Theory
On Risk-Averse Optimization
On Multi-Period Portfolio Optimization
Part 3: Some Special Topics
Special Topic: Stochastic Optimal Control Theory (if time permitted)
Special Topic: Stochastic Drawdown Risks (if time permitted)
Special Topic: Chance Constrained Optimization (if time permitted)
Prerequisites: Students planning to take this course should be fairly familiar with linear algebra, multivariate calculus, mathematical analysis, probability theory, statistics, and investment theory. Familiarity with numerical software such as Matlab or Python is also required. If in doubt about the background, the student should consult with the instructor.
Time and Place: Lectures are at T5T6T7, Room 204 TSMC Building.
Textbooks & References: Students will receive significant handout material to support the lectures. Below are some recommended textbooks; as we progress, other research papers will be assigned as reading tasks.
R. Xie and W. Wei, Distributionally Robust Optimization and its Applications, Springer, 2024.
A. Shapiro, D. Dentcheva, A. Ruszcynski, Lectures on Stochastic Programming: Modeling and Theory, SIAM, 2014.
A. Beck, Introduction to Nonlinear Optimization, SIAM, 2020.
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. (full-text link)
F. J. Fabozzi, P. N. Kolm, D. Pachamanova, S. M. Focardi, Robust Portfolio Optimization and Management, Wiley, 2007.
D. G. Luenberger, Optimization by Vector Space Methods, Wiley, 1976.
A. Ben-Tal, L. El. Ghaoui, and A. Nemirovski, Robust Optimization, Princeton University Press, 2009.
G. Cornuejols, J. Pena, R. Tütüncü, Optimization Methods in Finance, Cambridge University Press, 2018.
Teaching Method: Lecture.
Homework: Approximately bi-weekly.
Office Hours: By appointment.
Grading: The grade will be based on one late midterm (40%), homework (20%), and a special project (40%). The instructor may exercise discretion up to 10% in each grading category.
Tentative Schedule.
Week 01 (02/18)
Introduction to Optimization
Week 02 (02/25)
Convex Set
Week 03 (03/04)
Convex Function I
Week 04 (03/11)
Convex Function II
Week 05 (03/18)
Convex Optimization
Week 06 (03/25)
Robust and Stochastic Optimization I: SOCP
Week 07 (04/01)
Special Research Project: Topic Due.
Robust and Stochastic Optimization II: SDP
Week 08 (04/08)
Sensitivity of the Mean-Variance Model: Black-Litterman Approach
Week 09 (04/15)
Sensitivity of Mean-Variance Model: Robust Estimation
Week 10 (04/22)
Unconstrained Optimization Theory
Week 11 (04/29)
Duality Theory
Week 12 (05/06)
Special Research Project: Proposal Due.
Risk-Averse Optimization
Week 13 (05/13)
Risk-Averse Optimization
Week 14 (05/20)
Risk-Averse Optimization (Optional)
Week 15 (05/27)
Final Exam
Week 16 (06/03)
Final Project Due & Presentation
Handouts:
Additional Handout: A note on the limit of finite-dimensional l_p norm.
Chapter 5: Optimization Under Uncertainty: A Robust Approach
Chapter 6: Sensitivity of Mean-Variance Models and Black-Litterman Approaches
Chapter 7: Unconstrained Optimization Theory
Additional Handout: A short note on duality theory
Chapter 9: On Multi-Period Portfolio Optimization I: Kelly Criterion
Assignments
Assignment 01 (Due March 04)
Assignment 02 (Due March 11)
Assignment 03 (Due March 18)
Assignment 04 (Due March 26)
Assignment 05 (Due April 08)
Assignment 06 (Due April 22)
Assignment 07 (Due May 06)
Assignment 08 (Practice Only. No Need to Submit)
Assignment 09 (Practice Only. No Need to Submit)
Final Project Policies.
Your final project should include the following ingredients.
Title
Ensure it is concise, informative, and reflective of the project's main findings.
Abstract
Provide a succinct summary of the problem, methodology, main results, and conclusions.
Introduction
Provide a literature survey explaining what has been done, then point out what is missing in the literature (For example, say there is some weakness of the existing approach, so you want to fix it by providing your approach. As another example, say there is an issue that no one has noticed, so you jump in. As the last example, you found a phenomenon from your experiment/simulation/dataset, so you formed your hypothesis and wish to test it. This should provide enough ground to motivate your work. Then, provide the difference between your approach and others', and compare and contrast.
Problem Formulation or Preliminaries
If your work involves a theoretical setting, provide it in this section. Define every notion and the corresponding notations in a consistent and precise way. You should tell the reader exactly the main problem you want to tackle and the methodologies you adopted.
Main results or Empirical studies
The main claim or findings go first. Then, provide supporting evidence. For empirical studies, provide a detailed explanation about your data; e.g., where did you get the data? Why did you choose this dataset, not others? What do you see from the result? Are there any good or bad findings? If you run a simulation, describe how you conducted it precisely and concisely.
Concluding Remarks or/and Future Work
References
Your final project should be no more than 10 pages of A4 paper.
You are required to use LaTeX to write your project; Overleaf might be a handy editor.