论文标题
通过连续的凸近似算法解决高级投资组合
Solving High-Order Portfolios via Successive Convex Approximation Algorithms
论文作者
论文摘要
投资组合返回的第一时刻和第二个中央时刻，又称均值和差异，已被广泛用于评估投资组合的预期利润和风险。在设计投资组合时，投资者追求更高的均值和较低的差异。这两个时刻可以很好地描述投资组合收益的分布，当时它遵循高斯分布。但是，资产回报的现实世界分布通常是不对称的，重型的，这远非高斯分布。不对称性和重尾性的特征是第三和第四中心矩，即偏度和峰度。优选较高的偏度和较低的峰度，以减少极端损失的可能性。但是，由于其非跨性别性并随着尺寸迅速增加计算成本，因此在投资组合设计中融入高阶矩非常困难。在本文中，我们提出了一种基于连续的凸近似（SCA）算法的非常有效且可收敛的算法框架，以求解高阶投资组合。数值实验证明了所提出的算法框架的效率。
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments.
