求解大规模稀疏Min-CVaR投资组合模型的对偶方法

A dual method for solving large-scale sparse Min-CVaR portfolio selection model

投资组合管理需要在资产池中挑选合适的标的资产并确定投资组合配资比例,相关计算的时效性非常重要。基于L1范数的稀疏Min-CVaR(Minimum Conditional Value at Risk)模型可以同步完成挑选标的资产和确定配资比例,由于增加稀疏项,相比于标准Min-CVaR模型求解更复杂。为了有效求解大规模问题,基于原始模型中约束的结构特征,构造了其拉格朗日对偶模型,通过最新的商业求解器GUROBI 12.8求解对偶模型完成计算工作。使用基于三因子模型模拟的大规模情景数据(50 000行200列)和标普500高频交易数据(28 805行483列)进行了数值实验,结果显示对偶模型可以数倍提升计算效率,甚至比直接求解不具有稀疏性的标准MinCVaR模型更快。

Portfolio management requires selecting the right underlying asset in the asset pool and determining the proportion of the portfolio. The timeliness of calculations of the portfolio models is extremely important. The L1 norm sparse Min-CVaR(Minimum-CVaR, Conditional Value at Risk)model is able to simultaneously select the target assets and determine the capital allocation. Meanwhile,the L1 norm sparse Min-CVaR is harder to handle owing to the L1 norm regularization. In order to solve large-scale problems effectively, a Lagrangian dual model based on the structural features of constraints in the original model was constructed and solved by the state-of-the-art commercial solver GUROBI12.8. Numerical experiments were conducted on the simulated data(50 000 rows and 200 columns) and real-world data(the S&P 500: 28 805 rows and 483 columns). The numerical results show that,compared to the primal model, the dual method is several times faster than the primal method, and it is even faster than the standard Min-CVaR portfolio selection model without regularization.