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

摘要： 投资者在进行投资组合选择时，通常希望得到的投资组合方案中，被选择资产数量可控，风险水平足够小。模型中通常以基数约束来控制投资组合方案中选择的资产数量。基于一类基数约束投资组合选择模型，该模型以最小化风险函数为目标，在不允许卖空前题下，考虑基数约束和预算约束。该模型应用极其广泛，但目前尚无商用软件可以直接精确求解。提出一种全局最优化算法，在分支定界法框架基础上，以一阶算法求解下界松弛问题。通过Fama-French产业投资组合基准测试数据集设计仿真实验，实验结果表明，本文提出方法能有效解决带基数约束的产业投资组合问题，能够给出任意基数要求的全局最优投资组合方案。

关键词: 投资组合模型, 基数约束, 分支定界, 一阶算法