GAN-MP hybrid heuristic algorithm for non-convex portfolio optimization problem

Abstract

During recent decades, the traditional Markowitz model has been extended for asset cardinality, active share, and tracking-error constraints, which were introduced to overcome the drawbacks of the original Markowitz model. The resulting optimization problems, however, are often very difficult to solve, whereas those of the original Markowitz model are easily solvable. In order to resolve the portfolio optimization problem for the new extensions, we developed a novel heuristic algorithm that combines GAN (Generative Adversarial Networks) with mathematical programming: the GAN-MP hybrid heuristic algorithm. To the best of our knowledge, this is the first attempt to bridge neural networks (NN) and mathematical programming to tackle a real-world portfolio optimization problem. Computational experiments with real-life stock data show that our algorithm significantly outperforms the existing non-linear optimization solvers.

Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2015R1C1A1A01054606). The lead author (Chungmok Lee) also was supported by the Hankuk University of Foreign Studies (HUFS) Research Fund of 2018.

Additional information

Notes on contributors

Yerin Kim

Yerin Kim is a candidate for a Master’s degree in Industrial and Systems Engineering of KAIST. She graduated in Industrial and Management Engineering from the Hankuk University of Foreign Studies (HUFS). Her research interests diverge into two fields: 1) mathematical modeling of real-world problems and 2) development of optimization algorithms combined with other theories such as deep learning. She also has experience in constructing a system utilizing an optimization algorithm for a variant of the traveling salesman problem. Recognized for the excellence of that system, she received multiple awards from the Korea Ministry of Science and ICT in 2017.

Daemook Kang

Daemook Kang graduated in Industrial and Management Engineering from Hankuk University of Foreign Studies (HUFS). He was a team leader and an algorithm developer for a startup club, and was awarded the HUFS startup competition prize in 2017. His research interests include vehicle-route optimization, mathematical programming, data mining, and deep learning.

Mingoo Jeon

Mingoo Jeon is a senior at the Department of Industrial and Management Engineering, Hankuk University of Foreign Studies (HUFS). He is a recognized expert in Data Analysis Semi-Expert (ADsP) and Information Processing Skills. He was president of the Programming Club of HUFS. His research interests include algorithm development, data mining, web application development, and deep learning.

Chungmok Lee

Chungmok Lee is an associate professor at the Department of Industrial and Management Engineering, Hankuk University of Foreign Studies (HUFS). He completed his Ph.D. in Industrial Engineering at KAIST in 2009, and spent one year at RURCOR, Rutgers University, USA, as a visiting scholar. Before joining HUFS, he served as a research staff member at IBM Research-Ireland. His research articles appear in many prestigious journals including Operations Research, Mathematical Programming, Transportation Science, Transportation Research Part:B, INFORMS Journal on Computing, and Discrete Applied Mathematics. His awards include the Young Management Scientist Award from the Korean Operations Management Science Society in 2014 and the Research Division Award from IBM in 2014. His research interests span optimization-based interdisciplinary areas including mathematical programming, robust optimization, stochastic programming, and data mining.