Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
Abstract
We investigate mean-variance portfolio selection with an ℓ0-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit these properties in the risk minimization and return maximization formulations. Building on this structural insight, we develop a branch-and-bound algorithm tailored to the resulting robust sparse portfolio problems, together with a new pruning rule that can discard exponentially many candidate portfolios in a single step. Extensive computational experiments on real market data, together with comparisons against a mixed-integer second-order cone programming solver, demonstrate the effectiveness and competitiveness of the proposed approach.
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BibTeX
@misc{akkaya2026sparsity,
title = {{Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty}},
author = {Deniz Akkaya and Emre Can Yayla and Buse Şen and Mustafa Ç. Pınar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11749},
eprint = {2609.11749},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11749},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sparsity Regularized and Robust Mean Variance Portfolio Selection Under Ellipsoidal Uncertainty
AU - Deniz Akkaya
AU - Emre Can Yayla
AU - Buse Şen
AU - Mustafa Ç. Pınar
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11749
UR - https://arxiv.org/abs/2609.11749
AB - We investigate mean-variance portfolio selection with an ℓ_0-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit these properties in the risk minimization and return maximization formulations. Building on this structural insight, we develop a branch-and-bound algorithm tailored to the resulting robust sparse portfolio problems, together with a new pruning rule that can discard exponentially many candidate portfolios in a single step. Extensive computational experiments on real market data, together with comparisons against a mixed-integer second-order cone programming solver, demonstrate the effectiveness and competitiveness of the proposed approach.
ER -