论文标题
通过DCA和SCA稀疏的高级投资组合
Sparse High-Order Portfolios via Proximal DCA and SCA
论文作者
论文摘要
在本文中，我们旨在解决基础限制的高阶投资组合优化，即具有基数约束（MVSKC）的均值变化 - 稳态 - 库尔托病模型。 MVSKC模型的优化在两个部分中非常困难。一个是目标函数是非凸，另一个是基数约束的组合性质，导致非跨性别性和不连续性。 Based on the observation that cardinality constraint has the difference-of-convex (DC) property, we transform the cardinality constraint into a penalty term and then propose three algorithms including the proximal difference of convex algorithm (pDCA), pDCA with extrapolation (pDCAe) and the successive convex approximation (SCA) to handle the resulting penalized MVSK (PMVSK) formulation.此外，这些算法的理论收敛结果分别建立了。实际数据集上的数值实验证明了我们提出的方法在获得高效用和稀疏解决方案以及时间使用方面的效率。
In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two parts. One is that the objective function is non-convex, the other is the combinational nature of the cardinality constraint, leading to non-convexity as well dis-continuity. Based on the observation that cardinality constraint has the difference-of-convex (DC) property, we transform the cardinality constraint into a penalty term and then propose three algorithms including the proximal difference of convex algorithm (pDCA), pDCA with extrapolation (pDCAe) and the successive convex approximation (SCA) to handle the resulting penalized MVSK (PMVSK) formulation. Moreover, theoretical convergence results of these algorithms are established respectively. Numerical experiments on the real datasets demonstrate the superiority of our proposed methods in obtaining high utility and sparse solutions as well as efficiency in terms of time usage.
