关键词: 投资组合模型, 基数约束, 分支定界, 一阶算法

Abstract: Simplicity of portfolio selection is one of the main challenges faced by investors. In this paper, a family of portfolio model: minimizing risk function while considering cardinal constraint and budget constraint was considered. Besides, a branch and bound algorithm based on the branch and bound framework was proposed. Moreover, the relaxation problem was solved by using the first order method. Furthermore, computational experiments were conducted based on the Fama-French benchmark data. The computational results show that the algorithm proposed in this paper can effectively solve the problem of industrial investment portfolio with cardinality constraints, and can give a global optimal portfolio plan with arbitrary cardinality requirements.

Key words: portfolio selection model, cardinal constraint, branch and bound, first order method