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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.00605 |
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| _version_ | 1866917237212839936 |
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| author | Mousavi, Ahmad Salahi, Maziar Boukouvalas, Zois |
| author_facet | Mousavi, Ahmad Salahi, Maziar Boukouvalas, Zois |
| contents | This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The proposed algorithm solves a sequence of penalty subproblems using a block coordinate descent (BCD) method while striving to fully exploit each component within the objective function and constraints. Through rigorous analysis, the well-posedness of each subproblem of the BCD method is established, and closed-form solutions are derived where possible. A comprehensive theoretical convergence analysis is provided to confirm the efficacy of the introduced algorithm in reaching a Lu--Zhang minimizer for this intractable optimization problem. Numerical experiments conducted on real-world datasets validate the practical applicability and effectiveness of the introduced algorithm based on various criteria. Notably, the existence of closed-form solutions within the BCD subproblems prominently underscores the efficiency of our algorithm when compared to state-of-the-art methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Extended Mean-Variance-CVaR Portfolios with Short-selling Mousavi, Ahmad Salahi, Maziar Boukouvalas, Zois Optimization and Control This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The proposed algorithm solves a sequence of penalty subproblems using a block coordinate descent (BCD) method while striving to fully exploit each component within the objective function and constraints. Through rigorous analysis, the well-posedness of each subproblem of the BCD method is established, and closed-form solutions are derived where possible. A comprehensive theoretical convergence analysis is provided to confirm the efficacy of the introduced algorithm in reaching a Lu--Zhang minimizer for this intractable optimization problem. Numerical experiments conducted on real-world datasets validate the practical applicability and effectiveness of the introduced algorithm based on various criteria. Notably, the existence of closed-form solutions within the BCD subproblems prominently underscores the efficiency of our algorithm when compared to state-of-the-art methods. |
| title | Sparse Extended Mean-Variance-CVaR Portfolios with Short-selling |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.00605 |