ISSN Print: 2381-1196  ISSN Online: 2381-120X
International Journal of Investment Management and Financial Innovations  
Manuscript Information
 
 
Continuous Mean - Variance Portfolio Problem Is Studied with Time Delay Using Stochastic LQ Control Theory
International Journal of Investment Management and Financial Innovations
Vol.3 , No. 6, Publication Date: Dec. 6, 2017, Page: 58-66
853 Views Since December 6, 2017, 346 Downloads Since Dec. 6, 2017
 
 
Authors
 
[1]    

Yuquan Cui, School of Mathematics, Shandong University, Jinan, P.R. of China.

[2]    

Linlin Li, School of Mathematics, Shandong University, Jinan, P.R. of China.

[3]    

Cong Liu, School of Mathematics, Shandong University, Jinan, P.R. of China.

 
Abstract
 

The mean - variance portfolio selection model based on the expectation and variance of return on assets to measure the expected return and risk of investment. 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 optimal control theory, it established the discrete mean - variance time model with time delay. The paper has carried on the solution and example analysis. And according to the maximum principle, the optimal control model of the general form of the input delay stochastic LQ problem are obtained. The final result shows that when the delay is zero, the results is the same as the model without time delay


Keywords
 

The Mean - Variance Model, Portfolio Investment, Input Delay, Optimal Control, The Investment Strategy, Stochastic LQ Control


Reference
 
[01]    

H. Markowitz. Portfolio Selection [J]. Journal of Finance, 1952, 7 (1): 77-91.

[02]    

R. C. Merton. An Analytic Derivation of the Efficient Portfolio Frontier [J]. Journal of Finance& Quantitative Analysis, 1972, 7 (4): 1851-1872.

[03]    

G. P. Szego. Portfolio. Theory: with Application to Bank Asset Management [M]. Academic Press, 1980.

[04]    

Ye Zhongxing. Mathematical Finance [M]. Science Press, 2010.

[05]    

Wen-jing Guo. Dynamic Portfolio Investment Decision Model and Methods [M]. China Financial Publishing House, 2012.

[06]    

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.

[07]    

Zhuwu wu. Based on The Mean-Variance Framework of Portfolio Selection Model Research [D]. China Mining University, 2011.

[08]    

H. M. Markowitz. Portfolio Selection: Efficient Diversification of Investment [J]. Monograph. 1959.

[09]    

O. L. V. Costa, R. D. B. Nabholz. A Linear Matrix Inequalities Approach to Robust Mean semi-variance 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]    

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.

[22]    

L. Liu, P. Zhang. Dynamic Mean-variance Portfolio Selection with Liability No-Shorting Constraints [J]. Applied Mathematics Science, 2012, 40 (57-60): 2843-2849.

[23]    

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.

[24]    

X. Zhou, G. Yin. Continuous-Time Mean-variance Portfolio Selection with Regime Switching [C]. Proceedings of the IEEE Conference on Decision and Control. 2003: 383-388 vol. 1.

[25]    

Yunhui Xu, Zhongfei Li. Dynamic Portfolio Choice-Based on Income Sequence Related Dynamic Mean-variance model [J]. Journal of Systems Engineering Theory and Practice, 2008, 28 (8): 123-131.

[26]    

S. H. Wang. Application of Mean-variance Utility Function under the Portfolio Selection Decision [J]. Operations Research & Management Science, 2003.

[27]    

L. Chen, Z. Wu. Maximum Principle for the Stochastic Optimal Control Problem with Delay and Application [J]. Automatic, 2010, 46 (6): 1074-1080.

[28]    

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.

[29]    

Juanjuan Xu, Several Control Problem of Time-delay Systems Research [D], Shandong University, 2013.

[30]    

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.

[31]    

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.

[32]    

C. Li, Z. Wu. The Quadratic Problem for Stochastic Linear Control Systems with Delay [C]. Proceedings of the Chinese Control Conference, 2011, 1344-1349.





 
  Join Us
 
  Join as Reviewer
 
  Join Editorial Board
 
share:
 
 
Submission
 
 
Membership