论文标题
一般均值变化投资组合优化的快速连续QP算法
A Fast Successive QP Algorithm for General Mean-Variance Portfolio Optimization
论文作者
论文摘要
投资组合收益的平均值和差异是衡量投资组合的预期收益和风险的标准数量。有效的投资组合在均值和差异之间提供最佳的权衡。为了在这些有效的投资组合中表达偏爱，投资者提出了许多均匀变化的投资组合（MVP）配方，这些配方可以追溯到古典Markowitz Portfolio。但是，大多数现有的算法高度专注于特定的配方，并且不能推广到更广泛的应用。因此，快速而统一的算法将非常有益。在本文中，我们首先介绍了一般的MVP问题公式，可以通过探索它们的共同点来适合大多数现有情况。然后，我们为通用公式提出了一种广泛适用且可融合的连续二次编程算法（SCQP）。所提出的算法只能基于QP求解器实现，因此在计算上是有效的。此外，被认为是快速实施来加速算法。数值结果表明，我们提出的算法在收敛速度和可扩展性方面显着优于最先进的算法。
The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express a preference among these efficient portfolios, investors have put forward many mean-variance portfolio (MVP) formulations which date back to the classical Markowitz portfolio. However, most existing algorithms are highly specialized to particular formulations and cannot be generalized for broader applications. Therefore, a fast and unified algorithm would be extremely beneficial. In this paper, we first introduce a general MVP problem formulation that can fit most existing cases by exploring their commonalities. Then, we propose a widely applicable and provably convergent successive quadratic programming algorithm (SCQP) for the general formulation. The proposed algorithm can be implemented based on only the QP solvers and thus is computationally efficient. In addition, a fast implementation is considered to accelerate the algorithm. The numerical results show that our proposed algorithm significantly outperforms the state-of-the-art ones in terms of convergence speed and scalability.
