标题： 一种松弛优化方法用于 cardinality-constrained 投资组合优化 显示英文标题

标题： A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization

摘要： 受数量约束的组合限制了要交易的股票数量，无论是在整体上还是在各个组或行业中。 这些限制来自于基金经理在现实中面临的场景，他们在寻求最大化回报并限制风险时，受到交易成本和客户偏好的制约。 我们开发了一种新方法来解决受数量约束的组合优化问题，将数量约束扩展到马科维茨和条件风险价值（CVaR）优化模型中。 我们推导出一种连续松弛方法用于NP难的目标函数，这使得可以使用标准收敛保证的高效算法来处理非凸问题。 对于较小的案例，当暴力搜索可行以计算全局最优的受数量约束的组合时，新方法能够找到受数量约束的马科维茨模型的最佳组合，以及受数量约束的CVaR模型的一个非常好的局部最小值。 对于更高维度的情况，当暴力搜索代价过高时，我们找到了效率几乎与不受数量约束的组合相当的可行组合。 显示英文摘要

摘要： A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new approach to solve cardinality-constrained portfolio optimization problems, extending both Markowitz and conditional value at risk (CVaR) optimization models with cardinality constraints. We derive a continuous relaxation method for the NP-hard objective, which allows for very efficient algorithms with standard convergence guarantees for nonconvex problems. For smaller cases, where brute force search is feasible to compute the globally optimal cardinality- constrained portfolio, the new approach finds the best portfolio for the cardinality-constrained Markowitz model and a very good local minimum for the cardinality-constrained CVaR model. For higher dimensions, where brute-force search is prohibitively expensive, we find feasible portfolios that are nearly as efficient as their non-cardinality constrained counterparts.