论文标题
用于解决基数限制的均值组合优化问题的二重二元切面算法
Bilevel Cutting-plane Algorithm for Solving Cardinality-constrained Mean-CVaR Portfolio Optimization Problems
论文作者
论文摘要
本文使用条件价值（CVAR）作为风险度量研究了平均风险投资组合优化模型。我们还采用了基数限制来限制投资资产的数量。解决这样的基数受限的均值范围模型在计算上具有挑战性，原因有两个。首先，由于基数限制，该模型被称为混合企业优化（MIO）问题，因此，当可投资资产的数量较大时，解决该模型非常困难。其次，问题大小取决于资产返回场景的数量，当方案数量较大时，计算效率会降低。为了克服这些挑战，我们提出了一种名为\ emph {bilevel剪切平面算法}的高性能算法，以精确地解决了基数约束的均值均匀含量符号投资组合优化问题。我们首先将问题重新提出为双重优化问题，然后开发一种用于解决高层问题的切削平面算法。为了加快剪切生成的计算，我们适用于低级问题的另一种切削平面算法，可通过大量场景有效地最大程度地减少CVAR。此外，我们证明了双层切皮平面算法的收敛性。数值实验表明，与其他MIO方法相比，我们的算法可以更快地为大型问题实例提供最佳解决方案。
This paper studies mean-risk portfolio optimization models using the conditional value-at-risk (CVaR) as a risk measure. We also employ a cardinality constraint for limiting the number of invested assets. Solving such a cardinality-constrained mean-CVaR model is computationally challenging for two main reasons. First, this model is formulated as a mixed-integer optimization (MIO) problem because of the cardinality constraint, so solving it exactly is very hard when the number of investable assets is large. Second, the problem size depends on the number of asset return scenarios, and the computational efficiency decreases when the number of scenarios is large. To overcome these challenges, we propose a high-performance algorithm named the \emph{bilevel cutting-plane algorithm} for exactly solving the cardinality-constrained mean-CVaR portfolio optimization problem. We begin by reformulating the problem as a bilevel optimization problem and then develop a cutting-plane algorithm for solving the upper-level problem. To speed up computations for cut generation, we apply to the lower-level problem another cutting-plane algorithm for efficiently minimizing CVaR with a large number of scenarios. Moreover, we prove the convergence properties of our bilevel cutting-plane algorithm. Numerical experiments demonstrate that, compared with other MIO approaches, our algorithm can provide optimal solutions to large problem instances faster.
