本文考虑了摩擦市场下的多期证券投资组合选择问题,利用极小极大原理,建立了在含有机会成本和交易成本的多期极小极大投资组合选择模型.利用非线性规划相关理论, 证明了该模型最优解的存在性,并利用凸规划相关理论与Kuhn-Tucker条件给出了求解该模型的一种方法,最后通过实例对结论进行了说明.
Abstract
This paper deals with a multi-period portfolio selection problem in the frictional market. A multi-period minimax portfolio selection model with opportunity costs and transaction costs is proposed. By using the theory of nonlinear programming, we prove the existence of optimal solution of this model. Moreover, the method for solving this model is given by using the theory of convex programming and Kuhn-Tucker condition. Finally, a numerical example is given to illustrate our results.
关键词
投资组合 /
极小极大 /
机会成本 /
交易费用 /
凸优化
{{custom_keyword}} /
Key words
portfolio selection /
minimax /
opportunity costs /
transaction costs /
convex optimization
{{custom_keyword}} /
中图分类号：
F830.9
O221
{{custom_clc.code}}
({{custom_clc.text}})
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Markowitz H M. Foundations of portfolio theory[J]. Journal of Finance, 1991, 56(1): 469-477.
[2] Markowitz H M. Portfolio selection[J]. Journal of Finance, 1952, 7(1): 77-91.
[3] Deng X T, Li Z F, Wang S Y. A minimax portfolio selection strategy with equilibrium[J]. European Journal ofOperational Research, 2005, 166: 278-292.
[4] Wu Z W, Song X F, Xu Y Y, et al. A note on a minimax rule for portfolio selection and equilibrium pricesystem[J]. Applied Mathematics and Computation, 2009, 208: 49-57.
[5] Yan J F, Chen W F. A minimax portfolio selection strategy without risk-free asset[C] // Proceedings of 2008Chinese Control and Decision Conference, 2008: 2121-2125.
[6] Zhu K Y,Wu Z W. A note on a minimax rule for portfolio selection and equilibrium price system[C] // Proceedingsof 2008 International Conference on Risk and Reliability Management, 2008: 84-91.
[7] Zhu K Y, Wu Z W. The numerical algorithms to minimax portfolio selection model in frictional market[C] //Proceedings of rst International Conference of Modelling and Simulation, 2008, 4: 370-375.
[8] Mossin J. Optimal multiperiod portfolio policies[J]. Journal of Business, 1968, 41: 215-229.
[9] Chen A, Jen C, Zionts S. The optimal portfolio revision policy[J]. Journal of Business, 1971, 44: 51-61.
[10] Hakansson N H. Multi-period mean-variance analysis: Toward a general theory of portfolio choice[J]. Journal ofFinance, 1971, 26: 857-884.
[11] Dumas B, Luciano E. An exact solution to a dynamic portfolio choice problem under transaction costs[J]. Journalof Finance, 1991, 46: 577-595.
[12] Mulvey J M, Vladimirou H. Stochastic network programming for nancial planning problems[J]. ManagementScience, 1992, 38: 1642-1664.
[13] Dantzig G B, Infanger G. Multi-stage stochastic linear programs for portfolio optimization[J]. Annals of Opera-tions Research, 1993, 45: 59-76.
[14] Li D, Ng W L. Optimal dynamic portfolio selection: Multiperiod mean-variance formulation[J]. Journal ofFinance, 2000, 10: 387-406.
[15] Zhou X, Li D. Continuous-time mean-variance portfolio selection: A stochastic LQ framework[J]. Appl MathOptim, 2000, 42: 19-33.
[16] Zhou X, Yin G. Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model[J].SIAM J Control Optim, 2003, 42: 1466-1482.
[17] Celikyurt U, Ozekici S. Multiperiod portfolio optimization models in stochastic markets using the mean-varianceapproach[J]. European Journal of Operational Research, 2007, 179: 186-202.
[18] Costa O L V, Nabholz R B. Multiperiod mean-variance optimization with intertemporal restrictions[J]. J OptimTheory Appl, 2007, 134: 257-274.
[19] Edirisinghe N C P. Multiperiod portfolio optimization with terminal liability: Bounds for the convex case[J].Computational Optimization and Applications, 2005, 32: 29-59.
[20] Edirisinghe N C P, Patterson E I. Multi-period stochastic portfolio optimization: Block-separable decomposi-tion[J]. Ann Oper Res, 2007, 152: 367-394.
[21] Leippold M, Trojani F, Vanini P. A geometric approach to multiperiod mean variance optimization of assets andliabilities[J]. J Econ Dyn Control, 2004, 28: 1079-1113.
[22] Melkumian A A. The opportunity cost of being constrained by the type of asset: Bonds only or stocks only[J].Journal of Applied Economic, 2006, 9: 325-343.
[23] Simaan Y. What is the opportunity cost of mean-variance investment strategies?[J]. Management Science, 1993,39: 578-587.
[24] Tew B V, Reid D W, Witt C A. The opportunity cost of a mean-variance e cient choice[J]. Financial Review,1991, 26: 31-43.
[25] Fan K. Minimax theorems[J]. Proceedings of the National Academy of Sciences, USA, 1953, 39: 42-47.
[26] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear Programming: Theory and Algorithms[M]. New York: Wiley,1993.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
国家自然科学基金(70831005, 71101099);中央高校基本科研业务费(2009SCU11096)
{{custom_fund}}
PDF(449 KB)
