Course Syllabus

MFIT5009 – Optimization in FinTech

MSc in FinTech

Spring 2020-21, HKUST



This course introduces the basic theory of convex optimization and illustrates its practical employment in a wide range of FinTech applications. Techniques and applications of nonconvex optimization are also considered. Examples of the problems considered include Markowitz portfolio optimization and its many variations (e.g., maximum Sharpe ratio portfolio, risk-parity portfolio, robust portfolio, sparse portfolio, index tracking), the practical problem of data cleaning (imputation of missing values and outlier detection), machine learning, data clustering, and graph learning. Half of the course will focus on the mathematical foundation, while the other half will consider the practical implementation using the R programming language.


  • Yiyong Feng and Daniel P. Palomar, A Signal Processing Perspective on Financial Engineering. Foundations and Trends® in Signal Processing, Now Publishers, 2016. [pdf]
  • Konstantinos Benidis, Yiyong Feng, and Daniel P. Palomar, Optimization Methods for Financial Index Tracking: From Theory to Practice. Foundations and Trends® in Optimization, Now Publishers, 2018. [pdf]
  • Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [pdf]
  • G. James, D. Witten, T. Hastie, and R. Tibshirani. An Introduction to Statistical Learning with Applications in R. Springer, 2013. [pdf (Links to an external site.)]
  • G. Cornuejols and R. Tutuncu, Optimization Methods in Finance. Cambridge Univ. Press, 2007.


Good knowledge of linear algebra and some programming knowledge in R (or similar). Willingness to spend countless of hours programming in R.


Homework: 35%
Midterm:   15%
Final project: 35%
Final lightening presentation: 15% 

Course Schedule

Date Week Lect Topic
2-Feb     1    1 Theory: Introduction to convex optimization
   2 Practice: R for finance primer
9-Feb     2    3 Theory: Convex optimization problems
   4 Practice: Solvers in R
23-Feb     3    5 Portfolio optimization
   6      (cont’d)
2-Mar     4    7 Algorithms: Primer
   8 Algorithms: Majorization-Minimization (MM) and Successive Convex Approximation (SCA)
9-Mar     5    9 Index tracking of financial markets via MM
 10 Backtesting
16-Mar     6   - Midterm -
  - Midterm -
23-Mar     7  11 Risk parity portfolio via Newton, BCD, and SCA
 12      (cont’d)
30-Mar     8  13 Portfolio optimization with alternative risk measures
 14      (cont’d)
13-Apr    9  15 Supervised machine learning: Trees and random forests
 16      (cont’d)
20-Apr   10  17      (cont’d)
 18 Unsupervised machine learning: PCA
27-Apr  11 19 Unsupervised machine learning: Clustering
20      (cont’d)
4-May 12 21 Unsupervised machine learning: Graphs
22      (cont’d)
11-May  13 Project presentations by students
Project presentations by students

Lecture Information

Lecture Time: Tue 7pm – 9:50pm

Lecture Venue: Online via Zoom and, covid permitting, LSKG001

Teaching Team

Instructor: Prof. Daniel P. PALOMAR (


Office: 2398 (Lifts 17/18)

Office hours: By email appointment

TA: Xiwen WANG (

Course Summary:

Date Details Due