基于VaR风险控制的log-最优资产组合模型
摘要
本文考虑金融市场中的动态资产组合问题,以倍率-风险函数作为收益指标,风险价值(VaR)控制函数为风险指标,建立了基于VaR风险控制下的单周期动态log-最优资产组合模型,另外,应用动态规划方法建立了基于VaR风险控制下的多期动态log-最优资产组合模型,分析了模型的性质并证明了模型最优解的存在唯一性。应用遗传算法对两个模型分别进行了实证研究,并结合单周期和多周期两种情形进行比较分析,得出了在VaR风险和收益方面多期模型均要优于单周期模型的结论。
This thesis mainly discusses the dynamic portfolio of financial markets. A single-cycle dynamic log-optimal portfolio model was established by taking magnification-risk function as the revenue target, value at risk (VaR) control function as the risk indicators. Besides, A multi-cycle dynamic log-optimal portfolio model based on (VaR) risk control was also set up by applying dynamic programming methods, which analyzes the nature of the model and proves the unique existence of the model's optimal solutions. Empirical study about the two models has been done respectively. At last, a conclusion will be made that multi-cycle model are superior to single-cycle model in terms of the VaR risk and returns by comparing and analyzing single-cycle and multi-cycle models.
This thesis mainly discusses the dynamic portfolio of financial markets. A single-cycle dynamic log-optimal portfolio model was established by taking magnification-risk function as the revenue target, value at risk (VaR) control function as the risk indicators. Besides, A multi-cycle dynamic log-optimal portfolio model based on (VaR) risk control was also set up by applying dynamic programming methods, which analyzes the nature of the model and proves the unique existence of the model's optimal solutions. Empirical study about the two models has been done respectively. At last, a conclusion will be made that multi-cycle model are superior to single-cycle model in terms of the VaR risk and returns by comparing and analyzing single-cycle and multi-cycle models.
引文
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[15]刘莉,周霞,允许卖空的log-最优资产组合投资模型[J].应用数学,2002(2)：97～101.
[16]金秀,黄小原,马丽丽,基于VaR的多阶段金融资产配置模型[J].中国管理科学,2005(04)：13～16.
[17]李华昌,谢淑兰,易忠胜,遗传算法的原理与应用[J].矿冶2005(01)：87～90.
[18]刘勇,康立山,陈毓屏,非数值并行算法(第二册)——遗传算法[M].北京：科学出版社,2003.1～33.
[2]J. Mossion, Optimal Multiperiod Portfolio Policies[J]. Journal of Business.1968, 41:215～229.
[3]P.A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming[J]. Review of Economics and Statistics.1969,51:239～246.
[4]J. C. Mao, Models of capital budgeting. E-V versus E-S[J] Journal of Financial and Quantitative Analysis.1970,5(3):657～675.
[5]H. Konno, and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market [J]. Management Science.1991,37(5):519～531.
[6]X. Q. Cai, K. L. Teo, X. Q. Yang, X. Y. Zhou, Portfolio optimization under a minimax rule[J]. Management Science.2000,46(7):957～972.
[7]P. R. Kleindorfer, Multi-Period VaR-Constrained Portfolio Optimization with Applications to the Electric Power Sector[J]. Energy Journal-Cleveland. 2005.1～23.
[8]A. V. Puelz, A stochastic convergence model for fortfolio selection[J]. Operations Research.2002,50(3):462～476.
[9]L.C. Maclean, W. T. Ziemba, Growth versus security tradeoffs in dynamic invest analysis[J]. Annals of Operations Research.1999,85:193～225.
[10]D. Barro, E. Canestrelli, Dynamic portfolio optimization:Time decomposition using the Maximum Principle with a scenario approach[J]. European Journal of Operational Research.2005,163(1):217～229.
[11]叶中行,林建忠,数理金融-资产定价与金融决策理论[M].北京：科学出版社,2000.71～109.
[12]姚京,李仲飞,基于VaR的金融资产配置模型[J].中国管理科学.2004(12)：8～14.
[13]王春峰,金融市场风险管理[M]．第一版.天津：天津大学出版社,2001. 71～95.
[14]魏权龄,王日爽,徐兵,数学规划论[M].北京：北京航空航天大学出版社.1991.135～146.
[15]刘莉,周霞,允许卖空的log-最优资产组合投资模型[J].应用数学,2002(2)：97～101.
[16]金秀,黄小原,马丽丽,基于VaR的多阶段金融资产配置模型[J].中国管理科学,2005(04)：13～16.
[17]李华昌,谢淑兰,易忠胜,遗传算法的原理与应用[J].矿冶2005(01)：87～90.
[18]刘勇,康立山,陈毓屏,非数值并行算法(第二册)——遗传算法[M].北京：科学出版社,2003.1～33.