Abstract: Given a discrete portfolio selection model with roundlot constraint and concave transaction costs, we propose an exact algorithm for solving the model. The algorithm is of branch-and-bound method based on Lagrangian relaxation and subgradient dual search. To test the effectiveness of the algorithm, we carry out numerical experiments with randomly-generated data. For its application, this paper tests empirically the model with data from CSI300 Index and compares the computational results with those from the discrete portfolio selection model under non-transaction costs. The numerical analysis indicates that the proposed method can give portfolio strategy of the model within a reasonable time and is efficient for solving small-to-medium scale discrete portfolio selection problems.

Key words: operational research, portfolio strategy, branch-and-bound algorithm, Lagrangian dual

摘要： 本文建立带手数约束和凹交易费的离散投资组合模型,给出求解该模型的一种精确算法。该算法是一个基于拉格朗日松弛和次梯度对偶搜索的分枝定界算法。为测试算法的有效性,用随机产生的数据对模型进行数值实验。作为其应用,用沪深300指数的真实数据实证检验该模型,并与不含交易费用的离散投资组合模型进行数值比较分析。数值分析表明算法能在合理的时间内给出模型的投资组合策略, 对解决中小规模的离散投资组合问题是有效的。

关键词: 运筹学, 投资组合策略, 分枝定界算法, 拉格朗日对偶