American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Optimality conditions for vector equilibrium problems and their applications
  • JIMO Home
  • This Issue
  • Next Article
    Superconvergence for elliptic optimal control problems discretized by RT1 mixed finite elements and linear discontinuous elements
July  2013, 9(3): 643-656. doi: 10.3934/jimo.2013.9.643

Multi-period mean-variance portfolio selection with fixed and proportional transaction costs

Zhen Wang 1, and  Sanyang Liu 1,

1. 

Department of Mathematics, Xidian University, Xi'an, 710071, China, China

Received  May 2012 Revised  November 2012 Published  April 2013

Portfolio selection problem is one of the core research fields in modern financial economics. Considering the transaction costs in multi-period investments makes portfolio selection problems hard to solve. In this paper, the multi-period mean-variance portfolio selection problems with fixed and proportional transaction costs are investigated. By introducing the Lagrange multiplier and using the dynamic programming approach, the indirect utility function is defined for solving the portfolio selection problem constructed in this paper. The optimal strategies and the boundaries of the no-transaction region are obtained in the explicit form. And the efficient frontier for the original portfolio selection problems is also given. Numerical result shows that the method provided in this paper works well.
Keywords: dynamic programming, Optimal portfolio, transaction cost., mean-variance portfolio selection.
Mathematics Subject Classification: Primary: 90C39; Secondary: 91G1.
Citation: Zhen Wang, Sanyang Liu. Multi-period mean-variance portfolio selection with fixed and proportional transaction costs. Journal of Industrial & Management Optimization, 2013, 9 (3) : 643-656. doi: 10.3934/jimo.2013.9.643
References:
[1]

M. Akian, J. Menaldi and A. Sulem, On an investment-consumption model with transaction costs, Journal of Control and Optimization, 34 (1996), 329-364. doi: 10.1137/S0363012993247159.  Google Scholar

[2]

A. Balbas and S. Mayral, Nonconvex optimization for pricing and hedging in imperfect markets, Computers and Mathematics with Applications, 52 (2006), 121-136. doi: 10.1016/j.camwa.2006.08.009.  Google Scholar

[3]

D. Bertsimas and D. Pachamanova, Robust multiperiod portfolio management in the presence of transaction costs, Computers and Operations Research, 35 (2008), 3-17. doi: 10.1016/j.cor.2006.02.011.  Google Scholar

[4]

M. Best and J. Hlouskova, Quadratic programming with transaction costs, Computers $&$ Operations Research, 35 (2008), 18-33. doi: 10.1016/j.cor.2006.02.013.  Google Scholar

[5]

P. Boyle and X. Lin, Portfolio selection with transaction costs, North American Actuarial Journal, 1 (1997), 27-39. doi: 10.1080/10920277.1997.10595602.  Google Scholar

[6]

T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory, Journal of Economic Dynamics $&$ Control, 31 (2007), 2168-2195. doi: 10.1016/j.jedc.2006.06.006.  Google Scholar

[7]

U. Çlikyurt and S. Ökici, Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach, European Journal of Operational Research, 179 (2007), 186-202. Google Scholar

[8]

G. Constantinides, Optimal portfolio revision with proportional transaction costs: Extension to hara utility function and exogenous deterministic income, Management Science, 22 (1976), 921-923. doi: 10.1287/mnsc.22.8.921.  Google Scholar

[9]

M. Davis and A. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713. doi: 10.1287/moor.15.4.676.  Google Scholar

[10]

N. Framstad, B. Øksendal and A. Sulem, Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs, Journal of Mathematical Economics, 35 (2001), 233-257. doi: 10.1016/S0304-4068(00)00067-7.  Google Scholar

[11]

G. Gennotte and A. Jung, Investment strategies under transaction costs: The finite horizon case, Management Science, 40 (1994), 385-404. doi: 10.1287/mnsc.40.3.385.  Google Scholar

[12]

B. Jang, Optimal portfolio selection with transaction costs when an illiquid asset pays cash dividends, Journal of the Korean Mathematical Society, 44 (2007), 139-150. doi: 10.4134/JKMS.2007.44.1.139.  Google Scholar

[13]

J. Kamin, Optimal portfolio revision with a proportional transaction cost, Management Science, 21 (1975), 1263-1271. doi: 10.1287/mnsc.21.11.1263.  Google Scholar

[14]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market, Management Science, 37 (1991), 519-531. doi: 10.1287/mnsc.37.5.519.  Google Scholar

[15]

D. G. Luenberger, "Opitimization by Vector Space Methods," Wiley, New York, 1968.  Google Scholar

[16]

H. Markowitz, "Mean-Variance Analysis in Portfolio Choice and Capital Markets," Blackwell, Oxford, UK, 1992.  Google Scholar

[17]

R. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51 (1969), 247-257. doi: 10.2307/1926560.  Google Scholar

[18]

K. Muthuraman, A computational scheme for optimal investment-consumption with proportional transaction costs, Journal of Economic Dynamics $&$ Control, 31 (2007), 1132-1159. doi: 10.1016/j.jedc.2006.04.005.  Google Scholar

[19]

P. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246. doi: 10.2307/1926559.  Google Scholar

[20]

M. Woodside-Oriakhi, C. Lucas and J. E. Beasley, Portfolio rebalancing with an investment horizon and transaction costs, Omega, 41 (2013), 406-420. doi: 10.1016/j.omega.2012.03.003.  Google Scholar

[21]

H. Yao, A simple method for solving multiperiod mean-variance asset-liability management problem, Procedia Engineering, 23 (2011), 387-391. doi: 10.1016/j.proeng.2011.11.2518.  Google Scholar

[22]

L. Yi, Z. Li and D. Li, Multi-period portfolio selection for asset-liability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535-552. doi: 10.3934/jimo.2008.4.535.  Google Scholar

[23]

M. Yu, S. Takahashib, H. Inoueb and S. Wang, Dynamic portfolio optimization with risk control for absolute deviation model, European Journal of Operational Research, 201 (2010), 349-364. doi: 10.1016/j.ejor.2009.03.009.  Google Scholar

show all references

References:
[1]

M. Akian, J. Menaldi and A. Sulem, On an investment-consumption model with transaction costs, Journal of Control and Optimization, 34 (1996), 329-364. doi: 10.1137/S0363012993247159.  Google Scholar

[2]

A. Balbas and S. Mayral, Nonconvex optimization for pricing and hedging in imperfect markets, Computers and Mathematics with Applications, 52 (2006), 121-136. doi: 10.1016/j.camwa.2006.08.009.  Google Scholar

[3]

D. Bertsimas and D. Pachamanova, Robust multiperiod portfolio management in the presence of transaction costs, Computers and Operations Research, 35 (2008), 3-17. doi: 10.1016/j.cor.2006.02.011.  Google Scholar

[4]

M. Best and J. Hlouskova, Quadratic programming with transaction costs, Computers $&$ Operations Research, 35 (2008), 18-33. doi: 10.1016/j.cor.2006.02.013.  Google Scholar

[5]

P. Boyle and X. Lin, Portfolio selection with transaction costs, North American Actuarial Journal, 1 (1997), 27-39. doi: 10.1080/10920277.1997.10595602.  Google Scholar

[6]

T. Chellathurai and T. Draviam, Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory, Journal of Economic Dynamics $&$ Control, 31 (2007), 2168-2195. doi: 10.1016/j.jedc.2006.06.006.  Google Scholar

[7]

U. Çlikyurt and S. Ökici, Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach, European Journal of Operational Research, 179 (2007), 186-202. Google Scholar

[8]

G. Constantinides, Optimal portfolio revision with proportional transaction costs: Extension to hara utility function and exogenous deterministic income, Management Science, 22 (1976), 921-923. doi: 10.1287/mnsc.22.8.921.  Google Scholar

[9]

M. Davis and A. Norman, Portfolio selection with transaction costs, Mathematics of Operations Research, 15 (1990), 676-713. doi: 10.1287/moor.15.4.676.  Google Scholar

[10]

N. Framstad, B. Øksendal and A. Sulem, Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs, Journal of Mathematical Economics, 35 (2001), 233-257. doi: 10.1016/S0304-4068(00)00067-7.  Google Scholar

[11]

G. Gennotte and A. Jung, Investment strategies under transaction costs: The finite horizon case, Management Science, 40 (1994), 385-404. doi: 10.1287/mnsc.40.3.385.  Google Scholar

[12]

B. Jang, Optimal portfolio selection with transaction costs when an illiquid asset pays cash dividends, Journal of the Korean Mathematical Society, 44 (2007), 139-150. doi: 10.4134/JKMS.2007.44.1.139.  Google Scholar

[13]

J. Kamin, Optimal portfolio revision with a proportional transaction cost, Management Science, 21 (1975), 1263-1271. doi: 10.1287/mnsc.21.11.1263.  Google Scholar

[14]

H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to tokyo stock market, Management Science, 37 (1991), 519-531. doi: 10.1287/mnsc.37.5.519.  Google Scholar

[15]

D. G. Luenberger, "Opitimization by Vector Space Methods," Wiley, New York, 1968.  Google Scholar

[16]

H. Markowitz, "Mean-Variance Analysis in Portfolio Choice and Capital Markets," Blackwell, Oxford, UK, 1992.  Google Scholar

[17]

R. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, Review of Economics and Statistics, 51 (1969), 247-257. doi: 10.2307/1926560.  Google Scholar

[18]

K. Muthuraman, A computational scheme for optimal investment-consumption with proportional transaction costs, Journal of Economic Dynamics $&$ Control, 31 (2007), 1132-1159. doi: 10.1016/j.jedc.2006.04.005.  Google Scholar

[19]

P. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Review of Economics and Statistics, 51 (1969), 239-246. doi: 10.2307/1926559.  Google Scholar

[20]

M. Woodside-Oriakhi, C. Lucas and J. E. Beasley, Portfolio rebalancing with an investment horizon and transaction costs, Omega, 41 (2013), 406-420. doi: 10.1016/j.omega.2012.03.003.  Google Scholar

[21]

H. Yao, A simple method for solving multiperiod mean-variance asset-liability management problem, Procedia Engineering, 23 (2011), 387-391. doi: 10.1016/j.proeng.2011.11.2518.  Google Scholar

[22]

L. Yi, Z. Li and D. Li, Multi-period portfolio selection for asset-liability management with uncertain investment horizon, Journal of Industrial and Management Optimization, 4 (2008), 535-552. doi: 10.3934/jimo.2008.4.535.  Google Scholar

[23]

M. Yu, S. Takahashib, H. Inoueb and S. Wang, Dynamic portfolio optimization with risk control for absolute deviation model, European Journal of Operational Research, 201 (2010), 349-364. doi: 10.1016/j.ejor.2009.03.009.  Google Scholar

[1]

Yan Zeng, Zhongfei Li, Jingjun Liu. Optimal strategies of benchmark and mean-variance portfolio selection problems for insurers. Journal of Industrial & Management Optimization, 2010, 6 (3) : 483-496. doi: 10.3934/jimo.2010.6.483
[2]

Ping Chen, Haixiang Yao. Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching. Journal of Industrial & Management Optimization, 2020, 16 (2) : 531-551. doi: 10.3934/jimo.2018166
[3]

Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133
[4]

Ning Zhang. A symmetric Gauss-Seidel based method for a class of multi-period mean-variance portfolio selection problems. Journal of Industrial & Management Optimization, 2020, 16 (2) : 991-1008. doi: 10.3934/jimo.2018189
[5]

Shuang Li, Chuong Luong, Francisca Angkola, Yonghong Wu. Optimal asset portfolio with stochastic volatility under the mean-variance utility with state-dependent risk aversion. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1521-1533. doi: 10.3934/jimo.2016.12.1521
[6]

Xianping Wu, Xun Li, Zhongfei Li. A mean-field formulation for multi-period asset-liability mean-variance portfolio selection with probability constraints. Journal of Industrial & Management Optimization, 2018, 14 (1) : 249-265. doi: 10.3934/jimo.2017045
[7]

Yingxu Tian, Junyi Guo, Zhongyang Sun. Optimal mean-variance reinsurance in a financial market with stochastic rate of return. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1887-1912. doi: 10.3934/jimo.2020051
[8]

Ye Tian, Shucherng Fang, Zhibin Deng, Qingwei Jin. Cardinality constrained portfolio selection problem: A completely positive programming approach. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1041-1056. doi: 10.3934/jimo.2016.12.1041
[9]

Zhifeng Dai, Huan Zhu, Fenghua Wen. Two nonparametric approaches to mean absolute deviation portfolio selection model. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2283-2303. doi: 10.3934/jimo.2019054
[10]

Zhilin Kang, Xingyi Li, Zhongfei Li. Mean-CVaR portfolio selection model with ambiguity in distribution and attitude. Journal of Industrial & Management Optimization, 2020, 16 (6) : 3065-3081. doi: 10.3934/jimo.2019094
[11]

Peng Zhang, Yongquan Zeng, Guotai Chi. Time-consistent multiperiod mean semivariance portfolio selection with the real constraints. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1663-1680. doi: 10.3934/jimo.2020039
[12]

Yanqin Bai, Yudan Wei, Qian Li. An optimal trade-off model for portfolio selection with sensitivity of parameters. Journal of Industrial & Management Optimization, 2017, 13 (2) : 947-965. doi: 10.3934/jimo.2016055
[13]

Le Thi Hoai An, Tran Duc Quynh, Pham Dinh Tao. A DC programming approach for a class of bilevel programming problems and its application in Portfolio Selection. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 167-185. doi: 10.3934/naco.2012.2.167
[14]

Haixiang Yao, Zhongfei Li, Yongzeng Lai. Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate. Journal of Industrial & Management Optimization, 2016, 12 (1) : 187-209. doi: 10.3934/jimo.2016.12.187
[15]

Hao Chang, Jiaao Li, Hui Zhao. Robust optimal strategies of DC pension plans with stochastic volatility and stochastic income under mean-variance criteria. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021025
[16]

Peng Zhang. Multiperiod mean semi-absolute deviation interval portfolio selection with entropy constraints. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1169-1187. doi: 10.3934/jimo.2016067
[17]

Editorial Office. RETRACTION: Peng Zhang, Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 2019, 15 (2) : 537-564. doi: 10.3934/jimo.2018056
[18]

Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166
[19]

Ke Ruan, Masao Fukushima. Robust portfolio selection with a combined WCVaR and factor model. Journal of Industrial & Management Optimization, 2012, 8 (2) : 343-362. doi: 10.3934/jimo.2012.8.343
[20]

Hanqing Jin, Xun Yu Zhou. Continuous-time portfolio selection under ambiguity. Mathematical Control & Related Fields, 2015, 5 (3) : 475-488. doi: 10.3934/mcrf.2015.5.475

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (86)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences