发表机构
Bilkent University; EPFL（比尔肯特大学; 洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对椭球不确定性下的均值-方差投资组合选择，提出带$\ell_0$惩罚的稳健稀疏优化框架，刻画极值结构并设计分支定界算法及高效剪枝规则，实验验证其有效性与竞争力。
AI 中文摘要
我们研究了带有$\ell_0$惩罚项的均值-方差投资组合选择问题，以促进资产配置中的稀疏性。通过椭球不确定性集合来刻画均值回报向量中的不确定性，从而形成一个稳健的稀疏优化框架。我们刻画了局部和全局极小值的结构，并在风险最小化和收益最大化两种表述中利用这些性质。基于这一结构性洞见，我们开发了一种针对所得稳健稀疏投资组合问题的分支定界算法，并引入了一种新的剪枝规则，该规则可以在单步中丢弃指数多个候选投资组合。在真实市场数据上进行的大量计算实验，以及与混合整数二阶锥规划求解器的比较，证明了所提方法的有效性和竞争力。
英文摘要
We investigate mean-variance portfolio selection with an $\ell_0$-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.
