帯边际风险控制的投资组合问题的半定规划松弛  

Semidefinite programming relaxation for portfolio selection with marginal risk control

作　　者：丁晓东[1] 肖琳灿 罗和治[2] DING Xiaodong XIAO Lincan LUO Hezhi(College of Science, Zhejiang University of Technology, Hangzhou 310023, China College of Economics and Management, Zhejiang University of Technology, Hangzhou 310023, China)

机构地区：[1]浙江工业大学理学院,浙江杭州310023 [2]浙江工业大学经贸管理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2017年第1期64-68,共5页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(11371324);浙江省自然科学基金资助项目(LY17A010023)

摘　　要：边际风险衡量单个资产对投资组合总体风险的贡献,是投资组合和风险管理中的一个重要准则.考虑均值方差框架下带有边际风险控制的投资组合选择问题,其优化模型是一个非凸二次约束二次规划问题.通过探索模型的结构特点并结合提升方法和割不等式技术,给出了带有边际风险控制的均值方差投资组合选择模型的一个紧的半定规划松弛,分析了它与原问题的最优解和最优值之间的关系以及它与文献中的凸二次规划松弛所提供下界的比较关系.初步数值结果表明基于半定规划松弛的分支定界算法能有效地找到原问题的全局解.Marginal risk that is used to measure the contribution of an individual assets to the overall risk of the portfolio, is an important criterion in portfolio selection and risk management. In this paper, we consider the portfolio selection problem with marginal risk control in the mean- variance framework. In this problem, the optimization model is a quadratic programming problem with nonconvex quadratic constraints. By exploiting the structural characteristics of the model and combining the lifting method with secant inequality techniques, we present a tight semidefinite programming （SDP） relaxation for this problem. We discuss the relationships between optimal solutions and optimal values of the original problem and its SDP relaxation, and compare the lower bounds provided by the SDP relaxation and quadratic convex relaxation in the literature. Preliminary numerical results show that the branch-and-bound algorithm based on the SDP relaxation can find the global optimal solution of the original problem effectively.

关 键 词：投资组合 边际风险 半定规划松弛 分支定界 

分 类 号：O221.2[理学—运筹学与控制论]