| Citation: |
ZHANG Peng, CUI Shulin. Time-consistent Strategy Multiperiod Mean Standard Deviation Portfolio Selection[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(2): 91-99. DOI: 10.6054/j.jscnun.2024026
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The standard deviation is used to measure portfolio risk. Considering the transaction costs, borrowing constraints, and threshold constraints, a multiperiod mean standard deviation portfolio selection with the Vasicek stochastic interest rate model and risk preference is proposed. Based on the game theory, the model is transformed into a time-consistent dynamic programming problem. A novel discrete approximate iteration method is designed to obtain the optimal time-consistent portfolio strategy. Finally, the impact of borrowing constraints, threshold constraints, and different risk preference coefficients on multi-period mean standard deviation optimal time-consistent strategy are analyzed in empirical analysis. It can be concluded that the terminal wealth of the portfolio is positive, positive, and negative with borrowing constraints, threshold constraints, and risk preference coefficients, respectively. The unit risk of the portfolio is negative, negative, and positive with borrowing constraints, threshold constraints, and risk preference coefficients, respectively.
| [1] |
MARKOWITS H M. Portfolio selection[J]. Journal of finance, 1952, 7(1): 71-91.
|
| [2] |
周忠宝, 肖和录, 任甜甜, 等. 全链接分散化多阶段投资组合评价研究[J]. 管理科学学报, 2017, 20(6): 89-100. https://www.cnki.com.cn/Article/CJFDTOTAL-JCYJ201706007.htm
ZHOU Z B, XIAO H L, REN T T, et al. Performance eva-luation of multi-period portfolios via the fully linked diversification model[J]. Journal of Management Sciences in China, 2017, 20(6): 89-100. https://www.cnki.com.cn/Article/CJFDTOTAL-JCYJ201706007.htm
|
| [3] |
CUI X Y, GAO J J, SHI Y. Multi-period mean-variance portfolio optimization with management fees[J]. Operational Research, 2021, 21(2): 1333-1354. doi: 10.1007/s12351-019-00482-4
|
| [4] |
BJÖRK T, MURGOCI A, ZHOU X Y. Mean-variance port-folio optimization with state-dependent risk aversion[J]. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 2014, 24(1): 1-24.
|
| [5] |
郭文旌, 卢晖. 在不允许卖空市场条件下均值-方差投资者的最优时间一致性资产配置策略[J]. 系统管理学报, 2020, 29(2): 224-230. https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL202002004.htm
GUO W J, LU H. Optimal time-coinsistent asset allocation strategy for mean-variance investor with no short sel-ling[J]. Journal of Management Sciences in China, 2020, 29(2): 224-230. https://www.cnki.com.cn/Article/CJFDTOTAL-XTGL202002004.htm
|
| [6] |
张鹏, 李影, 曾永泉. 现实约束下多阶段模糊投资组合的时间一致性策略研究[J]. 中国管理科学, 2022, 30(4): 42-51. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK202204004.htm
ZHANG P, LI Y, ZENG Y Q. Time-cosistent strategy for the multiperiod fuzzy portfolio selection with real constraints[J]. Chinese Journal of Management Science, 2020, 30(4): 42-51. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK202204004.htm
|
| [7] |
VALLADÃO D, SILVA T, POGGI M. Time-consistent risk- constrained dynamic portfolio optimization with transactional costs and time-dependent returns[J]. Annals of Operations Research, 2019, 282(1): 379-405.
|
| [8] |
周忠宝, 任甜甜, 肖和录, 等. 基于相对财富效用的多阶段投资组合博弈模型[J]. 中国管理科学, 2019, 27(1): 34-43. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201901004.htm
ZHOU Z B, REN T T, XIAO H L, et al. Multi-period game model based on relative wealth utility[J]. Chinese Journal of Management Science, 2019, 27(1): 34-43. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201901004.htm
|
| [9] |
STRUB M S, LI D, CUI X, et al. Discrete-time mean-CVaR portfolio selection and time-consistency induced term structure of the CVaR[J]. Journal of Economic Dynamics and Control, 2019, 108: 103751/1-36.
|
| [10] |
YAO H X, LI Z F, LI D. Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability[J]. European Journal of Operational Research, 2016, 252(3): 837-851. doi: 10.1016/j.ejor.2016.01.049
|
| [11] |
李爱忠, 汪寿阳, 彭月兰. 考虑随机利率和通货膨胀的连续时间资产组合选择[J]. 中国管理科学, 2019, 27(2): 61-70. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201902007.htm
LI A Z, WANG S Y, PENG Y L. Continous-time asset allocation strategy with inflation and stochastic interest rates[J]. Chinese Journal of Management Science, 2019, 27(2): 61-70. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGK201902007.htm
|
| [12] |
WANG P, LI Z F. Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility[J]. Insurance: Mathematics and Economics, 2018, 80: 67-83. doi: 10.1016/j.insmatheco.2018.03.003
|
| [13] |
ZHANG L, LI D P, LAI Y Z. Equilibrium investment strategy for a defined contribution pension plan under stochastic interest rate and stochastic volatility[J]. Journal of Computational and Applied Mathematics, 2020, 368: 112536/1-35.
|
| [14] |
ZHU H N, ZHANG C K, JIN Z. Continuous-time mean-variance asset-liability management with stochastic inte-rest rates and inflation risks[J]. Journal of Industrial & Management Optimization, 2020, 16: 813-834.
|
| [15] |
ZHANG P, ZHANG W G. Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints[J]. Fuzzy Sets and Systems, 2014, 255: 74-91. doi: 10.1016/j.fss.2014.07.018
|
| [16] |
ZHANG P. Random credibilitic portfolio selection problem with different convex transaction costs[J]. Soft Computing, 2019, 23(24): 13309-13320. doi: 10.1007/s00500-019-03873-z
|
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