带二阶随机占优约束的投资组合优化问题的松弛割平面法

摘要

By combining the cutting plane method with Value at Risk (VaR) approximation,a relaxation cutting plane (RCP) method for portfolio optimization with second order dominance (SSD) constraints is proposed. The optimal value and optimal solutions of the relaxation method are approximation of the optimal value and optimal solutions of portfolio optimization with SSD constraints. The convergence analysis of the approximated solutions has been investigated when VaR confidence level β close to 1. Moreover,it is shown by testing empirically on two sets of market data that when VaR confidence level β less but close to 1,these portfolios constructed by the relaxation method outperform both the portfolios constructed by solving portfolio optimization problems with SSD constraints and index portfolios.%结合割平面法和风险价值(Value at Rick,VaR)近似方法,提出了一种松弛的割平面法,用来求解带二阶随机占优(Second order dominance,SSD)约束的投资组合优化问题,该松弛算法的最优值和解是带SSD约束的投资组合优化问题的近似最优值和近似解.随着VaR置信度β趋近于1,该近似解的收敛性被证明.两个市场数据的实证研究表明,当置信度β小于但接近于1时,松弛算法求得的投资组合的表现要优于带SSD约束的优化问题求得的投资组合的表现,优于相应的市场指数.