In this paper, the lower and upper admissible mean, downside semi-covariances and downside semi-variances of assets are first defined. Considering the transaction costs, borrowing constraints and threshold constraints, we present a new weighted lower and upper admissible mean downside semi-variance portfolio selection model which is a convex quadratic programming problem. The improved pivoting algorithm is presented to obtain the optimal portfolio strategy. Finally, the efficient frontiers comparison analyses of different optimistic coefficients, borrowing constraints and threshold constraints are given to examine the model and the designed algorithm.

中文翻译：

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加权的上下允许均值下半方差投资组合选择

在本文中，首先定义了资产的上下允许均值，下行半协方差和下行半方差。考虑交易成本，借款约束和门槛约束，我们提出了一个新的加权的上下可容许平均下行半方差投资组合选择模型，这是一个凸二次规划问题。提出了改进的数据透视算法，以获得最优的投资组合策略。最后，对不同的乐观系数，借用约束和阈值约束进行了有效的边界比较分析，以检验模型和设计算法。