Cardinality-constrained Distributionally Robust Portfolio Optimization
Abstract
This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by means of the moment-based ambiguity set of probability distributions of asset returns. To exactly solve large-scale problems, we propose a specialized cutting-plane algorithm that is based on bilevel optimization reformulation. We prove the finite convergence of the algorithm. We also apply a matrix completion technique to lower-level SDO problems to make their problem sizes much smaller. Numerical experiments demonstrate that our cutting-plane algorithm is significantly faster than the state-of-the-art MISDO solver SCIP-SDP. We also show that our portfolio optimization model can achieve good investment performance compared with the conventional robust optimization model based on the ellipsoidal uncertainty set.
Cite
@article{arxiv.2112.12454,
title = {Cardinality-constrained Distributionally Robust Portfolio Optimization},
author = {Ken Kobayashi and Yuichi Takano and Kazuhide Nakata},
journal= {arXiv preprint arXiv:2112.12454},
year = {2022}
}