| 考虑背景风险和流动性的模糊投资组合模型 |
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| 引用本文： | 宋慧慧,龙宪军,何光,彭再云.考虑背景风险和流动性的模糊投资组合模型[J].应用数学和力学,2021,42(2):212-220. |
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| 作者姓名： | 宋慧慧 龙宪军 何光 彭再云 |
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| 作者单位： | 1重庆工商大学 管理科学与工程学院, 重庆 400067;2重庆工商大学 数学与统计学院, 重庆 400067;3重庆交通大学 数学与统计学院, 重庆 400074 |
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| 基金项目： | 国家自然科学基金（面上项目）（11471059）；重庆市基础与前沿研究计划(重点项目)（cstc2018jcyjAX0119）；重庆市教育委员会科学技术研究计划(重点项目)（KJZD K201900801）；经济社会应用统计重庆市重点实验项目（KFJJ2017071）；重庆市巴渝学者特聘教授专项资助 |
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| 摘 要： | 利用投资收益率的二阶矩作为风险度量函数，建立了考虑背景风险和流动性的模糊投资组合模型.在满足预设收益率、换手率可能性均值要求水平以及风险资产的投资比例等约束条件下，使投资收益的二阶矩最小.最后选取中证100指数成分股中部分股票的历史数据进行数值分析，证明了该模型符合“高收益、高风险”的规律，说明该模型适用于实际金融市场.而且使用二阶矩代替方差作为风险度量函数，克服了方差计算复杂的缺陷，简化了模糊投资组合求解问题.
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| 关 键 词： | 背景风险 流动性 换手率 二阶矩 |
| 收稿时间： | 2019-10-12 |
A Fuzzy Portfolio Model With Background Risk and Liquidity Considered |
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| Institution: | 1School of Management Science and Engineering,Chongqing Technology and Business University, Chongqing 400067, P.R.China;2College of Mathematics and Statistics, Chongqing Technology and Business University,Chongqing 400067, P.R.China; |
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| Abstract: | With the 2nd moment of the investment return as the risk measurement function, a fuzzy portfolio model with the background risk and liquidity considered was established. The 2nd moment of the investment return was minimized under the constraint conditions satisfying the preset return rate, the average level of turnover probability and the investment proportion of risk assets. Finally, the historical data of some stocks in the 100 indices were selected for numerical analysis, and the model was proved to conform to the law of ‘high return and high risk’. The results show that, the model is suitable for the actual financial market. The 2nd moment instead of the variance as the risk measurement function, overcomes the complexity of variance calculation and simplifies the problem of fuzzy portfolio solution. |
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