doi: 10.3934/jimo.2018106

Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs

1. 

School of Business Administration, Hunan University, Changsha 410082, China

2. 

Business School, Hunan Normal University, Changsha 410081, China

3. 

Business School, University of Kent, Kent, CT2 7PE, UK

* Corresponding author: Zhongbao Zhou

Received  January 2018 Revised  March 2018 Published  July 2018

This paper investigates the multiperiod asset-liability management problem with quadratic transaction costs. Under the mean-variance criteria, we construct tractability models with/without the riskless asset and obtain the pre-commitment and time-consistent investment strategies through the application of embedding scheme and backward induction approach, respectively. In addition, some conclusions in the existing literatures can be regarded as the degenerated cases under our setting. Finally, the numerical simulations are given to show the difference of frontiers derived by different strategies. Also, some interesting findings on the impact of quadratic transaction cost parameters on efficient frontiers are discussed.

Citation: Zhongbao Zhou, Ximei Zeng, Helu Xiao, Tiantian Ren, Wenbin Liu. Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018106
References:
[1]

R. D. Arnott and W. H. Wagner, The measurement and control of trading costs, Financial Analysts Journal, 46 (1990), 73-80. doi: 10.2469/faj.v46.n6.73.

[2]

A. Bensoussan, K. C. Wong and S. C. P. Yam, Mean-variance pre-commitment policies revisited via a mean-field technique, in 2012 Recent Advances in Financial Engineering: Proceedings of the International Workshop on Finance, (2014), 177-198. doi: 10.1142/9789814571647_0008.

[3]

T. Bjork and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems, SSRN: 1694759. doi: 10.2139/ssrn.1694759.

[4]

S. BoydM. T. MuellerB. O'Donoghue and Y. Wang, Performance bounds and suboptimal policies for multi-period investment, Foundations and Trends in Optimization, 1 (2014), 1-72.

[5]

H. Chang, Dynamic mean-variance portfolio selection with liability and stochastic interest rate, Economic Modelling, 51 (2015), 172-182. doi: 10.1016/j.econmod.2015.07.017.

[6]

P. ChenH. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model, Insurance: Mathematics and Economics, 43 (2008), 456-465. doi: 10.1016/j.insmatheco.2008.09.001.

[7]

Z. P. ChenG. Li and J. E. Guo, Optimal investment policy in the time consistent mean-variance formulation, Insurance: Mathematics and Economics, 52 (2013), 145-156. doi: 10.1016/j.insmatheco.2012.11.007.

[8]

M. C. Chiu, Asset-liability management in continuous-time: Cointegration and exponential utility, Optimization and Control for Systems in the Big-Data Era, (2017), 85-100. doi: 10.1007/978-3-319-53518-0_6.

[9]

V. DeMiguelA. Martín-Utrera and F. J. Nogales, Parameter uncertainty in multiperiod portfolio optimization with transaction costs, Journal of Financial and Quantitative Analysis, 50 (2015), 1443-1471. doi: 10.1017/S002210901500054X.

[10]

Y. H. FuK. M. NgB. Huang and H. C. Huang, Portfolio optimization with transaction costs: A two-period mean-variance model, Annals of Operations Research, 233 (2015), 135-156. doi: 10.1007/s10479-014-1574-x.

[11]

N. Gârleanu and L. H. Pedersen, Dynamic trading with predictable returns and transaction costs, The Journal of Finance, 68 (2013), 2309-2340.

[12]

N. GülpinarD. Pachamanova and E. Çanakoğlu, A robust asset-liability management framework for investment products with guarantees, OR Spectrum, 38 (2016), 1007-1041. doi: 10.1007/s00291-016-0437-z.

[13]

S. GuoL. YuX. Li and S. Kar, Fuzzy multi-period portfolio selection with different investment horizons, European Journal of Operational Research, 254 (2016), 1026-1035. doi: 10.1016/j.ejor.2016.04.055.

[14]

A. Keel and H. H. Müller, Efficient portfolios in the asset liability context, ASTIN Bulletin: The Journal of the IAA, 25 (1995), 33-48. doi: 10.2143/AST.25.1.563252.

[15]

M. LeippoldF. Trojani and P. Vanini, A geometric approach to multiperiod mean variance optimization of assets and liabilities, Journal of Economic Dynamics and Control, 28 (2004), 1079-1113. doi: 10.1016/S0165-1889(03)00067-8.

[16]

D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod mean-variance formulation, Mathematical Finance, 10 (2000), 387-406. doi: 10.1111/1467-9965.00100.

[17]

C. Li and Z. Li, Multiperiod portfolio optimization for asset-liability management with bankrupt control, Applied Mathematics and Computation, 218 (2012), 11196-11208. doi: 10.1016/j.amc.2012.05.010.

[18]

X. LiS. Guo and L. Yu, Skewness of fuzzy numbers and its applications in portfolio selection, IEEE Transactions on Fuzzy Systems, 23 (2015), 2135-2143. doi: 10.1109/TFUZZ.2015.2404340.

[19]

J. Long and S. Zeng, Equilibrium time-consistent strategy for corporate international investment problem with mean-variance criterion, Mathematical Problems in Engineering, 2016 (2016), Art. ID 3295041, 20 pp. doi: 10.1155/2016/3295041.

[20]

H. Q. Ma, M. Wu and N. J. Huang, Time consistent strategies for mean-variance asset-liability management problems, Mathematical Problems in Engineering, 2013 (2013), Art. ID 709129, 16 pp.

[21]

H. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), 77-91.

[22]

M. Papi and S. Sbaraglia, Optimal asset-liability management with constraints: A dynamic programming approach, Applied Mathematics and Computation, 173 (2006), 306-349. doi: 10.1016/j.amc.2005.04.078.

[23]

R. W. Reid and S. J. Citron, On noninferior performance index vectors, Journal of Optimization Theory and Applications, 7 (1971), 11-28. doi: 10.1007/BF00933589.

[24]

W. F. Sharpe and L. G. Tint, Liabilities-A new approach, The Journal of Portfolio Management, 16 (1990), 5-10. doi: 10.3905/jpm.1990.409248.

[25]

L. M. Viceira, Bond risk, bond return volatility, and the term structure of interest rates, International Journal of Forecasting, 28 (2012), 97-117.

[26]

J. WeiK. C. WongS. C. P. Yam and S. P. Yung, Markowitz's mean-variance asset-liability management with regime switching: A time-consistent approach, Insurance: Mathematics and Economics, 53 (2013), 281-291. doi: 10.1016/j.insmatheco.2013.05.008.

[27]

H. Wu, Time-consistent strategies for a multiperiod mean-variance portfolio selection problem, Journal of Applied Mathematics, 2013 (2013), Art. ID 841627, 13 pp.

[28]

S. XieZ. Li and S. Wang, Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach, Insurance: Mathematics and Economics, 42 (2008), 943-953. doi: 10.1016/j.insmatheco.2007.10.014.

[29]

H. Yang and P. Chen, Markowitz's mean-variance asset-liability management with regime switching: A multiperiod model, Applied Mathematical Finance, 18 (2011), 29-50. doi: 10.1080/13504861003703633.

[30]

H. YaoZ. Li and S. Chen, Continuous-time mean-variance portfolio selection with only risky assets, Economic Modelling, 36 (2014), 244-251. doi: 10.1016/j.econmod.2013.09.041.

[31]

A. Yoshimoto, The mean-variance approach to portfolio optimization subject to transaction costs, Journal of the Operations Research Society of Japan, 39 (1996), 99-117. doi: 10.15807/jorsj.39.99.

[32]

L. YuS. Y. WangF. H. Wen and K. K. Lai, Genetic algorithm-based multi-criteria project portfolio selection, Annals of Operations Research, 197 (2012), 71-86. doi: 10.1007/s10479-010-0819-6.

[33]

L. YuS. Y. Wang and K. K. Lai, Multi-attribute portfolio selection with genetic optimization algorithms, INFOR: Information Systems and Operational Research, 47 (2009), 23-30. doi: 10.3138/infor.47.1.23.

[34]

L. YuS. Y. Wang and K. K. Lai, Neural network-based mean-variance -skewness model for portfolio selection, Computers and Operations Research, 35 (2008), 34-46. doi: 10.1016/j.cor.2006.02.012.

[35]

J. ZhangZ. Jin and Y. An, Dynamic portfolio optimization with ambiguity aversion, Journal of Banking and Finance, 79 (2017), 95-109. doi: 10.1016/j.jbankfin.2017.03.007.

[36]

X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 19-33. doi: 10.1007/s002450010003.

show all references

References:
[1]

R. D. Arnott and W. H. Wagner, The measurement and control of trading costs, Financial Analysts Journal, 46 (1990), 73-80. doi: 10.2469/faj.v46.n6.73.

[2]

A. Bensoussan, K. C. Wong and S. C. P. Yam, Mean-variance pre-commitment policies revisited via a mean-field technique, in 2012 Recent Advances in Financial Engineering: Proceedings of the International Workshop on Finance, (2014), 177-198. doi: 10.1142/9789814571647_0008.

[3]

T. Bjork and A. Murgoci, A general theory of Markovian time inconsistent stochastic control problems, SSRN: 1694759. doi: 10.2139/ssrn.1694759.

[4]

S. BoydM. T. MuellerB. O'Donoghue and Y. Wang, Performance bounds and suboptimal policies for multi-period investment, Foundations and Trends in Optimization, 1 (2014), 1-72.

[5]

H. Chang, Dynamic mean-variance portfolio selection with liability and stochastic interest rate, Economic Modelling, 51 (2015), 172-182. doi: 10.1016/j.econmod.2015.07.017.

[6]

P. ChenH. Yang and G. Yin, Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model, Insurance: Mathematics and Economics, 43 (2008), 456-465. doi: 10.1016/j.insmatheco.2008.09.001.

[7]

Z. P. ChenG. Li and J. E. Guo, Optimal investment policy in the time consistent mean-variance formulation, Insurance: Mathematics and Economics, 52 (2013), 145-156. doi: 10.1016/j.insmatheco.2012.11.007.

[8]

M. C. Chiu, Asset-liability management in continuous-time: Cointegration and exponential utility, Optimization and Control for Systems in the Big-Data Era, (2017), 85-100. doi: 10.1007/978-3-319-53518-0_6.

[9]

V. DeMiguelA. Martín-Utrera and F. J. Nogales, Parameter uncertainty in multiperiod portfolio optimization with transaction costs, Journal of Financial and Quantitative Analysis, 50 (2015), 1443-1471. doi: 10.1017/S002210901500054X.

[10]

Y. H. FuK. M. NgB. Huang and H. C. Huang, Portfolio optimization with transaction costs: A two-period mean-variance model, Annals of Operations Research, 233 (2015), 135-156. doi: 10.1007/s10479-014-1574-x.

[11]

N. Gârleanu and L. H. Pedersen, Dynamic trading with predictable returns and transaction costs, The Journal of Finance, 68 (2013), 2309-2340.

[12]

N. GülpinarD. Pachamanova and E. Çanakoğlu, A robust asset-liability management framework for investment products with guarantees, OR Spectrum, 38 (2016), 1007-1041. doi: 10.1007/s00291-016-0437-z.

[13]

S. GuoL. YuX. Li and S. Kar, Fuzzy multi-period portfolio selection with different investment horizons, European Journal of Operational Research, 254 (2016), 1026-1035. doi: 10.1016/j.ejor.2016.04.055.

[14]

A. Keel and H. H. Müller, Efficient portfolios in the asset liability context, ASTIN Bulletin: The Journal of the IAA, 25 (1995), 33-48. doi: 10.2143/AST.25.1.563252.

[15]

M. LeippoldF. Trojani and P. Vanini, A geometric approach to multiperiod mean variance optimization of assets and liabilities, Journal of Economic Dynamics and Control, 28 (2004), 1079-1113. doi: 10.1016/S0165-1889(03)00067-8.

[16]

D. Li and W. L. Ng, Optimal dynamic portfolio selection: Multiperiod mean-variance formulation, Mathematical Finance, 10 (2000), 387-406. doi: 10.1111/1467-9965.00100.

[17]

C. Li and Z. Li, Multiperiod portfolio optimization for asset-liability management with bankrupt control, Applied Mathematics and Computation, 218 (2012), 11196-11208. doi: 10.1016/j.amc.2012.05.010.

[18]

X. LiS. Guo and L. Yu, Skewness of fuzzy numbers and its applications in portfolio selection, IEEE Transactions on Fuzzy Systems, 23 (2015), 2135-2143. doi: 10.1109/TFUZZ.2015.2404340.

[19]

J. Long and S. Zeng, Equilibrium time-consistent strategy for corporate international investment problem with mean-variance criterion, Mathematical Problems in Engineering, 2016 (2016), Art. ID 3295041, 20 pp. doi: 10.1155/2016/3295041.

[20]

H. Q. Ma, M. Wu and N. J. Huang, Time consistent strategies for mean-variance asset-liability management problems, Mathematical Problems in Engineering, 2013 (2013), Art. ID 709129, 16 pp.

[21]

H. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), 77-91.

[22]

M. Papi and S. Sbaraglia, Optimal asset-liability management with constraints: A dynamic programming approach, Applied Mathematics and Computation, 173 (2006), 306-349. doi: 10.1016/j.amc.2005.04.078.

[23]

R. W. Reid and S. J. Citron, On noninferior performance index vectors, Journal of Optimization Theory and Applications, 7 (1971), 11-28. doi: 10.1007/BF00933589.

[24]

W. F. Sharpe and L. G. Tint, Liabilities-A new approach, The Journal of Portfolio Management, 16 (1990), 5-10. doi: 10.3905/jpm.1990.409248.

[25]

L. M. Viceira, Bond risk, bond return volatility, and the term structure of interest rates, International Journal of Forecasting, 28 (2012), 97-117.

[26]

J. WeiK. C. WongS. C. P. Yam and S. P. Yung, Markowitz's mean-variance asset-liability management with regime switching: A time-consistent approach, Insurance: Mathematics and Economics, 53 (2013), 281-291. doi: 10.1016/j.insmatheco.2013.05.008.

[27]

H. Wu, Time-consistent strategies for a multiperiod mean-variance portfolio selection problem, Journal of Applied Mathematics, 2013 (2013), Art. ID 841627, 13 pp.

[28]

S. XieZ. Li and S. Wang, Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach, Insurance: Mathematics and Economics, 42 (2008), 943-953. doi: 10.1016/j.insmatheco.2007.10.014.

[29]

H. Yang and P. Chen, Markowitz's mean-variance asset-liability management with regime switching: A multiperiod model, Applied Mathematical Finance, 18 (2011), 29-50. doi: 10.1080/13504861003703633.

[30]

H. YaoZ. Li and S. Chen, Continuous-time mean-variance portfolio selection with only risky assets, Economic Modelling, 36 (2014), 244-251. doi: 10.1016/j.econmod.2013.09.041.

[31]

A. Yoshimoto, The mean-variance approach to portfolio optimization subject to transaction costs, Journal of the Operations Research Society of Japan, 39 (1996), 99-117. doi: 10.15807/jorsj.39.99.

[32]

L. YuS. Y. WangF. H. Wen and K. K. Lai, Genetic algorithm-based multi-criteria project portfolio selection, Annals of Operations Research, 197 (2012), 71-86. doi: 10.1007/s10479-010-0819-6.

[33]

L. YuS. Y. Wang and K. K. Lai, Multi-attribute portfolio selection with genetic optimization algorithms, INFOR: Information Systems and Operational Research, 47 (2009), 23-30. doi: 10.3138/infor.47.1.23.

[34]

L. YuS. Y. Wang and K. K. Lai, Neural network-based mean-variance -skewness model for portfolio selection, Computers and Operations Research, 35 (2008), 34-46. doi: 10.1016/j.cor.2006.02.012.

[35]

J. ZhangZ. Jin and Y. An, Dynamic portfolio optimization with ambiguity aversion, Journal of Banking and Finance, 79 (2017), 95-109. doi: 10.1016/j.jbankfin.2017.03.007.

[36]

X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 19-33. doi: 10.1007/s002450010003.

Figure 1.  The M-V frontiers under different strategies with/without cost
Figure 2.  The M-V frontiers under different strategies
Figure 3.  The efficient frontiers of strategies under different costaversion coefficient
Figure 4.  The efficient frontiers of strategies under different parameter
Table 1.  The parameter set
$\Lambda^1$ $\Lambda^2$ $\Lambda^3$ $\Lambda^4$
$0.001 *\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 3& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 3& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 3 \end{bmatrix}$
$\Lambda^1$ $\Lambda^2$ $\Lambda^3$ $\Lambda^4$
$0.001 *\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 3& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 3& 0 \\ 0 & 0 & 1 \end{bmatrix}$ $0.001*\begin{bmatrix} 1& 0 & 0 \\ 0 & 1& 0 \\ 0 & 0 & 3 \end{bmatrix}$
[1]

Lan Yi, Zhongfei Li, Duan Li. Multi-period portfolio selection for asset-liability management with uncertain investment horizon. Journal of Industrial & Management Optimization, 2008, 4 (3) : 535-552. doi: 10.3934/jimo.2008.4.535

[2]

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

[3]

Dingjun Yao, Rongming Wang, Lin Xu. Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission. Journal of Industrial & Management Optimization, 2015, 11 (2) : 461-478. doi: 10.3934/jimo.2015.11.461

[4]

Linyi Qian, Lyu Chen, Zhuo Jin, Rongming Wang. Optimal liability ratio and dividend payment strategies under catastrophic risk. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1443-1461. doi: 10.3934/jimo.2018015

[5]

Yan Zhang, Yonghong Wu, Benchawan Wiwatanapataphee, Francisca Angkola. Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-31. doi: 10.3934/jimo.2018141

[6]

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

[7]

Dingjun Yao, Hailiang Yang, Rongming Wang. Optimal financing and dividend strategies in a dual model with proportional costs. Journal of Industrial & Management Optimization, 2010, 6 (4) : 761-777. doi: 10.3934/jimo.2010.6.761

[8]

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

[9]

Jemal Mohammed-Awel, Ruijun Zhao, Eric Numfor, Suzanne Lenhart. Management strategies in a malaria model combining human and transmission-blocking vaccines. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 977-1000. doi: 10.3934/dcdsb.2017049

[10]

Qian Zhao, Zhuo Jin, Jiaqin Wei. Optimal investment and dividend payment strategies with debt management and reinsurance. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1323-1348. doi: 10.3934/jimo.2018009

[11]

Giuseppe Maria Coclite, Mauro Garavello, Laura V. Spinolo. Optimal strategies for a time-dependent harvesting problem. Discrete & Continuous Dynamical Systems - S, 2018, 11 (5) : 865-900. doi: 10.3934/dcdss.2018053

[12]

Yang Shen, Tak Kuen Siu. Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 23-46. doi: 10.3934/jimo.2016002

[13]

Tao Pang, Azmat Hussain. An infinite time horizon portfolio optimization model with delays. Mathematical Control & Related Fields, 2016, 6 (4) : 629-651. doi: 10.3934/mcrf.2016018

[14]

Peng Zhang. Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection. Journal of Industrial & Management Optimization, 2018, 13 (5) : 1-28. doi: 10.3934/jimo.2018056

[15]

Min Dai, Zhou Yang. A note on finite horizon optimal investment and consumption with transaction costs. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1445-1454. doi: 10.3934/dcdsb.2016005

[16]

Ming-Jong Yao, Tien-Cheng Hsu. An efficient search algorithm for obtaining the optimal replenishment strategies in multi-stage just-in-time supply chain systems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 11-32. doi: 10.3934/jimo.2009.5.11

[17]

Xuemei Zhang, Malin Song, Guangdong Liu. Service product pricing strategies based on time-sensitive customer choice behavior. Journal of Industrial & Management Optimization, 2017, 13 (1) : 297-312. doi: 10.3934/jimo.2016018

[18]

Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030

[19]

Bruno Buonomo. A simple analysis of vaccination strategies for rubella. Mathematical Biosciences & Engineering, 2011, 8 (3) : 677-687. doi: 10.3934/mbe.2011.8.677

[20]

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

2017 Impact Factor: 0.994

Metrics

  • PDF downloads (27)
  • HTML views (301)
  • Cited by (0)

[Back to Top]