考虑背景风险和流动性的模糊投资组合模型

宋慧慧; 龙宪军; 何光; 彭再云

doi:10.21656/1000-0887.400298

考虑背景风险和流动性的模糊投资组合模型

doi: 10.21656/1000-0887.400298

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

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

详细信息

作者简介:
宋慧慧（1995—），女，硕士生(E-mail: songhuihui126@126.com);龙宪军（1980—），男，教授，博士(通讯作者. E-mail: xianjunlong@ctbu.edu.cn).

中图分类号: O224
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- 被引次数: 0
出版历程
- 收稿日期: 2019-10-12
- 修回日期: 2020-12-20
- 刊出日期: 2021-02-01

A Fuzzy Portfolio Model With Background Risk and Liquidity Considered

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;

Funds: The National Natural Science Foundation of China（11471059）

摘要

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.
- 背景风险 /
- 流动性 /
- 换手率 /
- 二阶矩
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.
- background risk /
- liquidity /
- turnover rate /
- 2nd moment

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参考文献(17)

[1]	MARKOWITZ H. Portfolio Selection: Efficient Diversification of Investments [M]. New York: Wiley, 1959.
[2]	ARNOTT R D, WAGNER W H. The measurement and control of trading costs[J]. Financial Analysis Journal,1990,46(6): 73-80.
[3]	MORTON A J, PLISKA S R. Optimal portfolio management with fixed transaction costs[J]. Mathematical Finance,1995,5(4): 337-336.
[4]	HUANG X X, YANG T T. How does background risk affect portfolio choice: an analysis based on uncertain mean-variance model with background risk[J]. Journal of Banking and Finance,2020,111: 105726.
[5]	HEATON J, LUCAS D. Market frictions, savings behavior, and portfolio choice[J]. Macroeconomic Dynamics,1997,1(1): 76-101.
[6]	李佳, 徐维军, 张卫国. 含有背景风险的双目标投资组合模型研究[J]. 运筹与管理, 2017,26(4): 118-123.(LI Jia, XU Weijun, ZHANG Weiguo. Bi objective portfolio selection model and algorithm with background risk[J]. Operations Research and Management Science,2017,26(4): 118-123.(in Chinese))
[7]	玄海燕, 金珍, 张玉春, 等. 基于背景风险的个人投资者投资决策研究[J]. 重庆师范大学学报(自然科学版), 2019,36(4): 93-99.(XUAN Haiyan, JIN Zhen, ZHANG Yuchun, et al. Research on investment decision of individual investors based on background risk[J]. Journal of Chongqing Normal University(Natural Sciences),2019,〖STHZ〗 36(4): 93-99.(in Chinese))
[8]	DUBOIS D, PRADE H. Possibility Theory: an Approach to Computerized Processing of Uncertainty [M]. Springer, 1988.
[9]	CARLSSON C, FULLER R. On possibilistic mean value and variance of fuzzy numbers[J]. Fuzzy Sets and Systems,2001,122(2): 315-326.
[10]	ZHANG W G, XIAO W L, XU W J. A possibilistic portfolio adjusting model with new added assets[J]. Economic Modelling,2010,27(1): 208-213.
[11]	李婷, 张卫国, 徐维军. 考虑背景风险因素的模糊投资组合选择模型[J]. 系统工程理论与实践, 2012,30(12): 33-38.(LI Ting, ZHANG Weiguo, XU Weijun. Fuzzy portfolio selection model considering background risk[J]. Theory and Practice of System Engineering,2012,30(12): 33-38.(in Chinese))
[12]	邓雄, 徐维军, 李佳, 等. 基于背景风险和弹性增量的模糊投资组合研究[J]. 数学的实践与认识, 2016,46(1): 38-46.(DENG Xiong, XU Weijun, LI Jia, et al. Research on fuzzy portfolio based on the background risk and elastic increment[J]. Practice and Understanding of Mathematics,2016,46(1): 38-46.(in Chinese))
[13]	李佳, 邓雄, 徐维军. 基于最大期望满意度与背景风险的模糊投资组合模型研究[J]. 数学的实践与认识, 2016,46(15): 140-149.(LI Jia, DENG Xiong, XU Weijun. Research on fuzzy portfolio model based on maximum expectation satisfaction and background risk[J]. Practice and Understanding of Mathematics,2016,46(15): 140-149.(in Chinese))
[14]	刘俊卿, 韩晶. 基于模糊数学理论的沥青路面结构可靠度分析[J]. 应用数学和力学, 2018,39(9): 1081-1090.(LIU Junqing, HAN Jing. Reliability analysis of asphalt pavement structure based on fuzzy mathematics theory[J]. Applied Mathematics and Mechanics,2018,39(9): 1081-1090.(in Chinese))
[15]	方勇, 汪寿阳. 模糊投资组合优化: 理论与方法[M]. 北京: 高等教育出版社, 2005.(FANG Yong, WANG Shouyang. Fuzzy Portfolio Optimization: Theory and Method [M]. Beijing: Higher Education Press, 2005.(in Chinese))
[16]	陈国华, 陈收, 方勇, 等. 带有模糊收益率的投资组合选择模型[J]. 系统工程理论与实践, 2009,29(7): 8-15.(CHEN Guohua, CHEN Shou, FANG Yong, et al. Portfolio selection model with fuzzy return[J]. Theory and Practice of System Engineering,2009,29(7): 8-15.(in Chinese))
[17]	刘彦奎, 白雪洁, 杨凯. 参数可信性优化方法[M]. 北京: 科学出版社, 2017.(LIU Yankui, BAI Xuejie, YANG Kai. Parameter Credibility Optimization Method [M]. Beijing: Science Press, 2017.(in Chinese))