手数约束和凹交易费下的离散投资组合模型及算法

Discrete Portfolio Selection Model and Algorithm under Roundlot Constraint and Concave Transaction Costs

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。

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 La- grangian relaxation and subgradient dual search. To test the effectiveness of the algorithm, we carry out numeri- cal experiments with randomly-generated data. For its application, this paper tests empirically the model with da- ta from CSI300 Index and compares the computational results with those from the discrete portfolio selection mod- el under non-transaction costs. The numerical analysis indicates that the proposed method can give portfolio strat- egy of the model within a reasonable time and is efficient for solving small-to-medium scale discrete portfolio se- lection problems.