Cardinality-constrained distributionally robust portfolio optimization

Ken Kobayashi, Yuichi Takano and Kazuhide Nakata

European Journal of Operational Research, 2023, vol. 309, issue 3, 1173-1182

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.

Keywords: Portfolio optimization; Mixed-integer semidefinite optimization; Distributionally robust optimization; Cutting-plane algorithm; Matrix completion (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:309:y:2023:i:3:p:1173-1182

DOI: 10.1016/j.ejor.2023.01.037

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