Due to the financial sector complicated variety of events, each financial problems from changes to know its essence, the change rule, from the change of strategy to formulate relevant policy and policy into effect, etc., the process inevitably has a certain lag. Therefore, in order to better reflect the actual situation, we study the portfolio model with delays in this paper. By joining our delay control item, the optimization model was established, the goal is to maximize earnings expectations. In this paper, it studies the continuous time without delay the mean - variance portfolio problems on the basis of existing research. It established auxiliary problem using the stochastic linear quadratic optimal control theory. Using the maximum principle, the solution of the optimal investment strategy are given and it analysis the case, the conclusion is in conformity with the actual. It studies the existing time delay portfolio strategy problem in discrete time case. Based on the stochastic LQ (linear quadratic) optimal control theory, it established the discrete time model with time delay. The paper has carried on the solution and example analysis.
| Published in | Mathematics and Computer Science (Volume 2, Issue 6) |
| DOI | 10.11648/j.mcs.20170206.13 |
| Page(s) | 98-112 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
The Mean - Variance Model, Portfolio Investment, Input Delay, Optimal Control, Investment Strategy
| [1] | H. Markowitz. Portfolio Selection [J]. Journal of Finance, 1952, 7(1): 77-91. |
| [2] | R. C. Merton. An Analytic Derivation of the Efficient Portfolio Frontier [J]. Journal of Finance& Quantitative Analysis, 1972, 7(4): 1851-1872. |
| [3] | G. P. Szego. Portfolio. Theory: with Application to Bank Asset Management [M]. Academic Press, 1980. |
| [4] | Ye Zhongxing. Mathematical Finance [M]. Science Press, 2010. |
| [5] | Wenjing Guo. Dynamic Portfolio Investment Decision Model and Methods [M]. China Financial Publishing House, 2012. |
| [6] | Dequan Yang, Deli Yang, Kelu Shi, etc. To Solve are Not Allowed to Sell Short the Interval of The Portfolio Frontier Search Method [J]. Journal of Management Science, 2001 (1): 33-37. |
| [7] | Zhuwu wu. Based on The Mean-Variance Framework of Portfolio Selection Model Research [D]. China Mining University, 2011. |
| [8] | H. M. Markowitz. Portfolio Selection: Efficient Diversification of Investment [J]. Monograph. 1959. |
| [9] | O. L. V. Costa, R. D. B. Nabholz. A Linear Matrix Inequalities Approach to Robust Mean-semivariance Portfolio Optimization [J]. Applied Optimization, 2002, 74: 89-107. |
| [10] | Enrique Ballestero. Mean semi-variance Efficient Frontier: A Downside Risk Model for Portfolio Selection [J]. Applied Mathematical Finance, 2005, 12(1): 1-15. |
| [11] | F. C. Jen, S. Zionts. The Optimal Portfolio Revision Policy [J]. Journal of Business, 1971, 44(1): 51-61. |
| [12] | D. Li, Wan. Optimal Dynamic Portfolio Selection: Multi-Period Mean-variance Formulation [J]. Social Science Electronic Publishing, 1998, 10(3): 387-406. |
| [13] | Yao Haiyang, Ginger Sensitive, Ma Qinghua etc. Serial Correlation Risk Assets Income Multi-stage Mean-Variance Portfolio Selection [J]. Control and Decision, 2014 (7): 1226-1231. |
| [14] | M. V. Araujo, V. C. O. L. Do. Discrete-time Mean-variance Optimization with Markov Switching Parameters [C]. Proceedings of the American Control Conference, 2006, 2487-2497. |
| [15] | G. Yin, X. Zhou. Markowitz’s Mean-variance Portfolio Selection with Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits [J]. Automatic Control, IEEE Transaction on, 2004, 49(3):349-360. |
| [16] | X. Zhou, D. Li. Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework [J]. Applied Mathematics &Optimization, 2000, 42(1): 19-33. |
| [17] | X. Zhou, D. Li. Explicit Efficient Frontier of a Continuous-Time Mean-variance Portfolio Selection Problem [J]. Ifip Advances in Information &Communication Technology, 1998, 13:323-330. |
| [18] | A. E. B. Lim, X. Zhou. Mean-variance Portfolio with Random Parameters [J]. Mathematical of Operations Research, 2002, 27(1):101-120. |
| [19] | W. Guo. H. Yan. M. Lei. Mean-variance Optimal Portfolio Selection with Random Parameters and Discontinuous Stock Prices [J]. Applied Mathematical A Journal of Chinese Universities, 2007, 3(3):263-269. |
| [20] | X. Li, X. Zhou, A. E. B. Lim. Dynamic Mean-variance Optimal Portfolio Selection with No-Shorting Constraints [J], Siam Journal on Control & Optimization, 2002, 40(5): 1540-1555. |
| [21] | C. Mei, D. Li. Asset and Liability Management under a Continuous-Time Mean-variance Optimization Framework [J]. Insurance Mathematics &Economics, 2006, 39(3): 330-355. |
| [22] | S. Xie, Z. Li, S. Wang. Continuous-Time Portfolio Selection with Liability: Mean-variance Model and Stochastic LQ Approach [J]. Insurance Mathematics &Economics, 2008, 42(3): 943-953. |
| [23] | L. Liu, P. Zhang. Dynamic Mean-variance Portfolio Selection with Liability No-Shorting Constraints [J]. Applied Mathematics Science, 2012, 40(57-60): 2843-2849. |
| [24] | T. R. Bielecki, H. Jin, S. R. Pliska, et al. Continuous-Time Mean-variance Portfolio Selection with Bankruptcy Prohibition [J]. Mathematics Finance, 2005, 15(2): 213-214. |
| [25] | R. C. Merton. Optimum Consumption and Portfolio Rules in Continuous-Time Model [J]. Journal of Economic Theory, 1971, 3(71): 373-413. |
| [26] | R. C. Merton, P. A. Samuelson. Continuous-Time Finance [M]. B. Blackwell, 1990. |
| [27] | S. H. Wang. Application of Mean-variance Utility Function under the Portfolio Selection Decision [J]. Operations Research & Management Science, 2003. |
| [28] | J. C. Cox. C. F. Huang. Optimal Consumption and Portfolio Policies when Asset Prices follow a Diffusion Process [J]. Journal of Economic Theory, 1989, 49(1): 33-83. |
| [29] | O. S. Alp, R. Korn. Continuous-Time Mean-variance Portfolio Optimization in a Jump-diffusion Market [J]. Decisions in Economic & Finance, 2011, 34(1): 21-40. |
| [30] | D. M. Dang, P. A. Forsyth. Continuous-Time Mean-variance Optimal Portfolio Allocation under Jump-diffusion: An Numerical Impulse Control Approach [J]. Numerical Methods for Partial Differential Equations, 2014, 30(2): 664-698. |
| [31] | Y. Xu, Z. Wu. Li. Continuous-Time Mean-variance Mean variance Portfolio Selection with Inflation in an Incomplete Market [J]. Journal of Financial Risk Management, 2014, 03(02): 19-28. |
| [32] | W. Pang, Y. Ni, X. Li, et al. Continuous-Time Mean-variance Mean variance Portfolio Selection with Partial Information [J]. Journal of Mathematical Financial, 2014, 03(5): 353-365. |
| [33] | S. Yang. Mean-variance Mean variance Portfolio Selection in a Complete Market with Unbounded Random Coefficients [J]. Automatic, 2015, 55:165-175. |
| [34] | L. Chen, Z. Wu. Maximum Principle for the Stochastic Optimal Control Problem with Delay and Application [J]. Automatic, 2010, 46(6): 1074-1080. |
| [35] | X. Song, H. Zhang, L. Xie. Linear Quadratic Regulation for Discrete-Time Stochastic System with Input Delay [C]. The 27th Session of the Chinese Control Conference Proceedings, 2008:2008-436. |
| [36] | Juanjuan Xu, Several Control Problem of Time-delay Systems Research [D], Shandong University, 2013. |
| [37] | H. Zhang, L. Li, J. Xu, et al. Linear Quadratic Regulation and Stabilization of Discrete-Time System [J]. Automatic Control IEEE Transactions on. 2015, 60(10): 1. |
| [38] | S. Chen, X. Li, X. Zhou. Stochastic Linear Quadratic Regulation with Indefinite Control Weight Costs [J]. Siam Journal on Control & Optimization, 2000, 39(4): 1065-1081. |
| [39] | C. Li, Z. Wu. The Quadratic Problem for Stochastic Linear Control Systems with Delay [C]. Proceedings of the Chinese Control Conference, 2011, 1344-1349. |
APA Style
Yuquan Cui, Linlin Li, Hua Liu. (2017). The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay. Mathematics and Computer Science, 2(6), 98-112. https://doi.org/10.11648/j.mcs.20170206.13
ACS Style
Yuquan Cui; Linlin Li; Hua Liu. The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay. Math. Comput. Sci. 2017, 2(6), 98-112. doi: 10.11648/j.mcs.20170206.13
AMA Style
Yuquan Cui, Linlin Li, Hua Liu. The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay. Math Comput Sci. 2017;2(6):98-112. doi: 10.11648/j.mcs.20170206.13
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Download@article{10.11648/j.mcs.20170206.13,
author = {Yuquan Cui and Linlin Li and Hua Liu},
title = {The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay},
journal = {Mathematics and Computer Science},
volume = {2},
number = {6},
pages = {98-112},
doi = {10.11648/j.mcs.20170206.13},
url = {https://doi.org/10.11648/j.mcs.20170206.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170206.13},
abstract = {Due to the financial sector complicated variety of events, each financial problems from changes to know its essence, the change rule, from the change of strategy to formulate relevant policy and policy into effect, etc., the process inevitably has a certain lag. Therefore, in order to better reflect the actual situation, we study the portfolio model with delays in this paper. By joining our delay control item, the optimization model was established, the goal is to maximize earnings expectations. In this paper, it studies the continuous time without delay the mean - variance portfolio problems on the basis of existing research. It established auxiliary problem using the stochastic linear quadratic optimal control theory. Using the maximum principle, the solution of the optimal investment strategy are given and it analysis the case, the conclusion is in conformity with the actual. It studies the existing time delay portfolio strategy problem in discrete time case. Based on the stochastic LQ (linear quadratic) optimal control theory, it established the discrete time model with time delay. The paper has carried on the solution and example analysis.},
year = {2017}
}
TY - JOUR T1 - The Research of Discrete Mean - Variance Portfolio Problem with Time-Delay AU - Yuquan Cui AU - Linlin Li AU - Hua Liu Y1 - 2017/11/22 PY - 2017 N1 - https://doi.org/10.11648/j.mcs.20170206.13 DO - 10.11648/j.mcs.20170206.13 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 98 EP - 112 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20170206.13 AB - Due to the financial sector complicated variety of events, each financial problems from changes to know its essence, the change rule, from the change of strategy to formulate relevant policy and policy into effect, etc., the process inevitably has a certain lag. Therefore, in order to better reflect the actual situation, we study the portfolio model with delays in this paper. By joining our delay control item, the optimization model was established, the goal is to maximize earnings expectations. In this paper, it studies the continuous time without delay the mean - variance portfolio problems on the basis of existing research. It established auxiliary problem using the stochastic linear quadratic optimal control theory. Using the maximum principle, the solution of the optimal investment strategy are given and it analysis the case, the conclusion is in conformity with the actual. It studies the existing time delay portfolio strategy problem in discrete time case. Based on the stochastic LQ (linear quadratic) optimal control theory, it established the discrete time model with time delay. The paper has carried on the solution and example analysis. VL - 2 IS - 6 ER -
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