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arXiv · 2112.12454

Cardinality-constrained Distributionally Robust Portfolio Optimization

Ken Kobayashi·Yuichi Takano·Kazuhide Nakata
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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.

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Ken Kobayashi, Yuichi Takano, Kazuhide Nakata. 2021-12-23. Cardinality-constrained Distributionally Robust Portfolio Optimization. https://arxiv.org/abs/2112.12454

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