Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

Lihua Bian; Zhongfei Li; Haixiang Yao

doi:10.3934/jimo.2020026

Previous Article
Machine interference problem involving unsuccessful switchover for a group of repairable servers with vacations
JIMO Home
This Issue
Next Article
Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach

May 2021, 17(3): 1383-1410. doi: 10.3934/jimo.2020026

Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

Lihua Bian ^1,2, , Zhongfei Li ^3,4,, and Haixiang Yao ^5,

1.	School of Finance and Economics, Qinghai University, Xining 810016, PR China
2.	School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China
3.	Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China
4.	School of Management, Xinhua College of Sun Yat-sen University, Guangzhou 510520, China
5.	School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China

^* Corresponding author: Zhongfei Li

Received December 2018 Revised October 2019 Published May 2021 Early access February 2020

Fund Project: This research is supported by the National Natural Science Foundation of China (Nos. 71721001, 71871071, 71471045), the Natural Science Foundation of Guangdong Province of China (Nos. 2014A030312003, 2017A030313399, 2018B030311004), the Innovation Team Project of Guangdong Colleges and Universities (No. 2016WCXTD012), and the Innovative School Project in Higher Education of Guangdong Province of China (No. GWTP-GC-2017-03)

In this paper, we investigate a multi-period mean-variance asset-liability management problem with stochastic interest rate and seek its time-consistent strategy. The financial market is assumed to be composed of one risk-free asset and multiple risky assets, and the stochastic interest rate is characterized by the discrete-time Vasicek model proposed by Yao et al. (2016a)[38]. We regard this problem as a non-cooperative game whose equilibrium strategy is the desired time-consistent strategy. We derive the analytical expressions of the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by the extended Bellman equation. Some special cases of our model are discussed, and some properties of our equilibrium strategy, including a two-fund separation theorem, are proposed. Finally, a numerical example with real data is given to illustrate our theoretical results.

Keywords: Multi-period mean-variance model, Time-consistent strategy, Asset-liability management, Stochastic interest rate, Game theory.

Mathematics Subject Classification: Primary: 91G10, 93C55; Secondary: 93E20.

Citation: Lihua Bian, Zhongfei Li, Haixiang Yao. Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1383-1410. doi: 10.3934/jimo.2020026

References:

[1]	L. H. Bian, Z. F. Li and H. X. Yao, Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause, Insurance: Mathematics and Economics, 81 (2018), 78-94. doi: 10.1016/j.insmatheco.2018.05.005.
[2]	T. Björk, M. Khapko and A. Murgoci, On time-inconsistent stochastic control in continuous time, Finance and Stochastics, 21 (2017), 331-360. doi: 10.1007/s00780-017-0327-5.
[3]	T. Björk and A. Murgoci, A theory of Markovian time-inconsitent stochastic control in discrete time, Finance and Stochastics, 18 (2014), 545-592. doi: 10.1007/s00780-014-0234-y.
[4]	C. 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.
[5]	P. Chen and H. L. Yang, Markowitz's mean-variance asset-liability management with regime switching: A multi-period model, Applied Mathematical Finance, 18 (2011), 29-50. doi: 10.1080/13504861003703633.
[6]	P. Chen, H. L. 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]	M. C. Chiu and H. Y. Wong, Mean-variance asset-liability management with asset correlation risk and insurance liabilities, Insurance: Mathematics and Economics, 59 (2014), 300-310. doi: 10.1016/j.insmatheco.2014.10.003.
[8]	R. Ferland and F. Watier, Mean-variance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 71-84. doi: 10.1002/asmb.767.
[9]	D. Hainaut, Dynamic asset allocation under VaR constraint with stochastic interest rates, Annals of Operations Research, 172 (2009), 97-117. doi: 10.1007/s10479-008-0509-9.
[10]	L. He and Z. X. Liang, Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework, Insurance: Mathematics and Economics, 53 (2013), 643-649. doi: 10.1016/j.insmatheco.2013.09.002.
[11]	R. Korn and H. Kraft, A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40 (2002), 1250-1269. doi: 10.1137/S0363012900377791.
[12]	M. Leippold, F. Trojani and P. Vanini, A geomeric 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.
[13]	M. Leippold, F. Trojani and P. Vanini, Multiperiod mean-variance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 1535-1546. doi: 10.1080/14697680902950813.
[14]	C. J. Li and Z. F. Li, Multi-period 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.
[15]	C. J. Li, Z. F. Li, K. Fu and H. Q. Song, Time-consistent optimal portfolio strategy for asset-liability management under mean-variance criterion, Accounting and Finance Research, 2 (2013), 89-104. doi: 10.5430/afr.v2n2p89.
[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]	Z. X. Liang and M. Ma, Optimal dynamic asset allocation of pension fund in mortality and salary risks framework, Insurance: Mathematics and Economics, 64 (2015), 151-161. doi: 10.1016/j.insmatheco.2015.05.008.
[18]	A. Lioui and P. Poncet, On optimal portfolio choice under stochastic interest rates, Journal of Economic Dynamics and Control, 25 (2001), 1841-1865. doi: 10.1016/S0165-1889(00)00005-1.
[19]	H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
[20]	F. Menoncin and E. Vigna, Mean-variance target-based optimization for defined contribution pension schemes in a stochastic framework, Insurance: Mathematics and Economics, 76 (2017), 172-184. doi: 10.1016/j.insmatheco.2017.08.002.
[21]	R. J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley, New York, 1982.
[22]	C. Munk and C. Sørensen, Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96 (2010), 433-462.
[23]	S. Mushtaq and D. A. Siddiqui, Effect of interest rate on economic performance: Evidence from Islamic and non-Islamic economies, Financial Innovation, 2 (2016), 2-9. doi: 10.1186/s40854-016-0028-7.
[24]	J. Pan and Q. X. Xiao, Optimal asset-liability management with liquidity constraints and stochastic interest rates in the expected utility framework, Journal of Computational and Applied Mathematics, 317 (2017a), 371-387. doi: 10.1016/j.cam.2016.11.037.
[25]	J. Pan and Q. X. Xiao, Optimal mean-variance asset-liability management with stochastic interest rates and inflation risks, Mathematical Methods of Operations Research, 85 (2017b), 491-519. doi: 10.1007/s00186-017-0580-6.
[26]	W. F. Sharpe and L. G. Tint, Liabilities-a new approach, Journal of Portfolio Management, 16 (1990), 5-10. doi: 10.3905/jpm.1990.409248.
[27]	Y. Shen and T. K. Siu, Asset allocation under stochastic interest rate with regime switching, Economic Modelling, 29 (2012), 1126-1136. doi: 10.1016/j.econmod.2012.03.024.
[28]	R. Strotz, Myopia and inconsistency in dynamic utility maximization, Readings in Welfare Economics, (1973), 128–143. doi: 10.1007/978-1-349-15492-0_10.
[29]	J. Y. Sun, Z. F. Li and Y. Zeng, Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump-diffusion model, Insurance: Mathematics and Economics, 67 (2016), 158-172. doi: 10.1016/j.insmatheco.2016.01.005.
[30]	J. Tobin, Liquidity preference as behavior toward risk, Review of Economic Studies, 67 (1958), 65-86. doi: 10.2307/2296205.
[31]	J. Wei and T. X. Wang, Time-consistent mean-variance asset-liability management with random coefficients, Insurance: Mathematics and Economics, 77 (2017), 84-96. doi: 10.1016/j.insmatheco.2017.08.011.
[32]	J. Wei, K. C. Wong, S. C. P. Yam and S. P. Yung, Liquidity preference as behavior toward risk, Review of Economic Studies, 67 (1958), 65-86.
[33]	H. L. Wu, Time-consistent strategies for a multiperiod mean-variance portfolio selection problem, Journal of Applied Mathematics, 2013 (2013), Art. ID 841627, 13 pp. doi: 10.1155/2013/841627.
[34]	H. L. Wu and H. Chen, Nash equilibrium strategy for a multi-period mean-variance portfolio selection problem with regime switching, Economic Modelling, 46 (2015), 79-90. doi: 10.1016/j.econmod.2014.12.024.
[35]	S. X. Xie, Continuous-time mean-variance portfolio selection with liability and regime switching, Insurance: Mathematics and Economics, 45 (2009), 148-155. doi: 10.1016/j.insmatheco.2009.05.005.
[36]	H. X. Yao, X. Li, Z. F. Hao and Y. Li, Dynamic asset-liability management in a Markov market with stochastic cash flows, Quantitative Finance, 16 (2016b), 1575-1597. doi: 10.1080/14697688.2016.1151070.
[37]	H. X. Yao, Z. F. Li and Y. Z. Lai, Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate, Journal of Industrial and Management Optimization, 12 (2016c), 187-209. doi: 10.3934/jimo.2016.12.187.
[38]	H. X. Yao, Z. F. Li and D. Li, Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability, European Journal of Operational Research, 252 (2016a), 837-851. doi: 10.1016/j.ejor.2016.01.049.
[39]	H. X. Yao, Y. Zeng and S. M. Chen, Multi-period mean-variance asset-liability management with uncontrolled cash flow and uncertain time-horizon, Economic Modelling, 30 (2013), 492-500. doi: 10.1016/j.econmod.2012.10.004.
[40]	F. Z. Zhang, Matrix Theory: Basic Results and Techniques, 2$^{nd}$ edition, Springer-Verlag, New York, 2011.
[41]	L. Zhang, H. Zhang and H. X. Yao, Optimal investment management for a defined contribution pension fund under imperfect information, Insurance: Mathematics and Economics, 79 (2018), 210-224. doi: 10.1016/j.insmatheco.2018.01.007.
[42]	X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics Optimization, 42 (2000), 19-33. doi: 10.1007/s002450010003.

show all references

References:

[1]	L. H. Bian, Z. F. Li and H. X. Yao, Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause, Insurance: Mathematics and Economics, 81 (2018), 78-94. doi: 10.1016/j.insmatheco.2018.05.005.
[2]	T. Björk, M. Khapko and A. Murgoci, On time-inconsistent stochastic control in continuous time, Finance and Stochastics, 21 (2017), 331-360. doi: 10.1007/s00780-017-0327-5.
[3]	T. Björk and A. Murgoci, A theory of Markovian time-inconsitent stochastic control in discrete time, Finance and Stochastics, 18 (2014), 545-592. doi: 10.1007/s00780-014-0234-y.
[4]	C. 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.
[5]	P. Chen and H. L. Yang, Markowitz's mean-variance asset-liability management with regime switching: A multi-period model, Applied Mathematical Finance, 18 (2011), 29-50. doi: 10.1080/13504861003703633.
[6]	P. Chen, H. L. 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]	M. C. Chiu and H. Y. Wong, Mean-variance asset-liability management with asset correlation risk and insurance liabilities, Insurance: Mathematics and Economics, 59 (2014), 300-310. doi: 10.1016/j.insmatheco.2014.10.003.
[8]	R. Ferland and F. Watier, Mean-variance efficiency with extended CIR interest rates, Applied Stochastic Models in Business and Industry, 26 (2010), 71-84. doi: 10.1002/asmb.767.
[9]	D. Hainaut, Dynamic asset allocation under VaR constraint with stochastic interest rates, Annals of Operations Research, 172 (2009), 97-117. doi: 10.1007/s10479-008-0509-9.
[10]	L. He and Z. X. Liang, Optimal investment strategy for the DC plan with the return of premiums clauses in a mean-variance framework, Insurance: Mathematics and Economics, 53 (2013), 643-649. doi: 10.1016/j.insmatheco.2013.09.002.
[11]	R. Korn and H. Kraft, A stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40 (2002), 1250-1269. doi: 10.1137/S0363012900377791.
[12]	M. Leippold, F. Trojani and P. Vanini, A geomeric 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.
[13]	M. Leippold, F. Trojani and P. Vanini, Multiperiod mean-variance efficient portfolios with endogenous liabilities, Quantitative Finance, 11 (2011), 1535-1546. doi: 10.1080/14697680902950813.
[14]	C. J. Li and Z. F. Li, Multi-period 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.
[15]	C. J. Li, Z. F. Li, K. Fu and H. Q. Song, Time-consistent optimal portfolio strategy for asset-liability management under mean-variance criterion, Accounting and Finance Research, 2 (2013), 89-104. doi: 10.5430/afr.v2n2p89.
[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]	Z. X. Liang and M. Ma, Optimal dynamic asset allocation of pension fund in mortality and salary risks framework, Insurance: Mathematics and Economics, 64 (2015), 151-161. doi: 10.1016/j.insmatheco.2015.05.008.
[18]	A. Lioui and P. Poncet, On optimal portfolio choice under stochastic interest rates, Journal of Economic Dynamics and Control, 25 (2001), 1841-1865. doi: 10.1016/S0165-1889(00)00005-1.
[19]	H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
[20]	F. Menoncin and E. Vigna, Mean-variance target-based optimization for defined contribution pension schemes in a stochastic framework, Insurance: Mathematics and Economics, 76 (2017), 172-184. doi: 10.1016/j.insmatheco.2017.08.002.
[21]	R. J. Muirhead, Aspects of Multivariate Statistical Theory, John Wiley, New York, 1982.
[22]	C. Munk and C. Sørensen, Dynamic asset allocation with stochastic income and interest rates, Journal of Financial Economics, 96 (2010), 433-462.
[23]	S. Mushtaq and D. A. Siddiqui, Effect of interest rate on economic performance: Evidence from Islamic and non-Islamic economies, Financial Innovation, 2 (2016), 2-9. doi: 10.1186/s40854-016-0028-7.
[24]	J. Pan and Q. X. Xiao, Optimal asset-liability management with liquidity constraints and stochastic interest rates in the expected utility framework, Journal of Computational and Applied Mathematics, 317 (2017a), 371-387. doi: 10.1016/j.cam.2016.11.037.
[25]	J. Pan and Q. X. Xiao, Optimal mean-variance asset-liability management with stochastic interest rates and inflation risks, Mathematical Methods of Operations Research, 85 (2017b), 491-519. doi: 10.1007/s00186-017-0580-6.
[26]	W. F. Sharpe and L. G. Tint, Liabilities-a new approach, Journal of Portfolio Management, 16 (1990), 5-10. doi: 10.3905/jpm.1990.409248.
[27]	Y. Shen and T. K. Siu, Asset allocation under stochastic interest rate with regime switching, Economic Modelling, 29 (2012), 1126-1136. doi: 10.1016/j.econmod.2012.03.024.
[28]	R. Strotz, Myopia and inconsistency in dynamic utility maximization, Readings in Welfare Economics, (1973), 128–143. doi: 10.1007/978-1-349-15492-0_10.
[29]	J. Y. Sun, Z. F. Li and Y. Zeng, Precommitment and equilibrium investment strategies for defined contribution pension plans under a jump-diffusion model, Insurance: Mathematics and Economics, 67 (2016), 158-172. doi: 10.1016/j.insmatheco.2016.01.005.
[30]	J. Tobin, Liquidity preference as behavior toward risk, Review of Economic Studies, 67 (1958), 65-86. doi: 10.2307/2296205.
[31]	J. Wei and T. X. Wang, Time-consistent mean-variance asset-liability management with random coefficients, Insurance: Mathematics and Economics, 77 (2017), 84-96. doi: 10.1016/j.insmatheco.2017.08.011.
[32]	J. Wei, K. C. Wong, S. C. P. Yam and S. P. Yung, Liquidity preference as behavior toward risk, Review of Economic Studies, 67 (1958), 65-86.
[33]	H. L. Wu, Time-consistent strategies for a multiperiod mean-variance portfolio selection problem, Journal of Applied Mathematics, 2013 (2013), Art. ID 841627, 13 pp. doi: 10.1155/2013/841627.
[34]	H. L. Wu and H. Chen, Nash equilibrium strategy for a multi-period mean-variance portfolio selection problem with regime switching, Economic Modelling, 46 (2015), 79-90. doi: 10.1016/j.econmod.2014.12.024.
[35]	S. X. Xie, Continuous-time mean-variance portfolio selection with liability and regime switching, Insurance: Mathematics and Economics, 45 (2009), 148-155. doi: 10.1016/j.insmatheco.2009.05.005.
[36]	H. X. Yao, X. Li, Z. F. Hao and Y. Li, Dynamic asset-liability management in a Markov market with stochastic cash flows, Quantitative Finance, 16 (2016b), 1575-1597. doi: 10.1080/14697688.2016.1151070.
[37]	H. X. Yao, Z. F. Li and Y. Z. Lai, Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate, Journal of Industrial and Management Optimization, 12 (2016c), 187-209. doi: 10.3934/jimo.2016.12.187.
[38]	H. X. Yao, Z. F. Li and D. Li, Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability, European Journal of Operational Research, 252 (2016a), 837-851. doi: 10.1016/j.ejor.2016.01.049.
[39]	H. X. Yao, Y. Zeng and S. M. Chen, Multi-period mean-variance asset-liability management with uncontrolled cash flow and uncertain time-horizon, Economic Modelling, 30 (2013), 492-500. doi: 10.1016/j.econmod.2012.10.004.
[40]	F. Z. Zhang, Matrix Theory: Basic Results and Techniques, 2$^{nd}$ edition, Springer-Verlag, New York, 2011.
[41]	L. Zhang, H. Zhang and H. X. Yao, Optimal investment management for a defined contribution pension fund under imperfect information, Insurance: Mathematics and Economics, 79 (2018), 210-224. doi: 10.1016/j.insmatheco.2018.01.007.
[42]	X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics Optimization, 42 (2000), 19-33. doi: 10.1007/s002450010003.

Figure 1. The equilibrium strategies with and without liability

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. The surplus process of the equilibrium strategies with and without liability

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. The effect of liability on the equilibrium strategy

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4. The effect of stochastic interest rate on the equilibrium strategy

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5. A comparison of the equilibrium strategy and precommitment strategy

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6. The effect of liability on the equilibrium efficient frontier

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7. The effect of stochastic interest rate on the equilibrium efficient frontier

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 8. A comparison of the equilibrium efficient frontier and pre-commitment efficient frontier

Figure Options

Download full-size image

Download as PowerPoint slide

[1]	Huai-Nian Zhu, Cheng-Ke Zhang, Zhuo Jin. Continuous-time mean-variance asset-liability management with stochastic interest rates and inflation risks. Journal of Industrial and Management Optimization, 2020, 16 (2) : 813-834. doi: 10.3934/jimo.2018180
[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 and Management Optimization, 2018, 14 (1) : 249-265. doi: 10.3934/jimo.2017045
[3]	Zhiping Chen, Jia Liu, Gang Li. Time consistent policy of multi-period mean-variance problem in stochastic markets. Journal of Industrial and Management Optimization, 2016, 12 (1) : 229-249. doi: 10.3934/jimo.2016.12.229
[4]	Lan Yi, Zhongfei Li, Duan Li. Multi-period portfolio selection for asset-liability management with uncertain investment horizon. Journal of Industrial and Management Optimization, 2008, 4 (3) : 535-552. doi: 10.3934/jimo.2008.4.535
[5]	Haixiang Yao, Zhongfei Li, Yongzeng Lai. Dynamic mean-variance asset allocation with stochastic interest rate and inflation rate. Journal of Industrial and Management Optimization, 2016, 12 (1) : 187-209. doi: 10.3934/jimo.2016.12.187
[6]	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 and Management Optimization, 2020, 16 (1) : 71-101. doi: 10.3934/jimo.2018141
[7]	Zhen Wang, Sanyang Liu. Multi-period mean-variance portfolio selection with fixed and proportional transaction costs. Journal of Industrial and Management Optimization, 2013, 9 (3) : 643-657. doi: 10.3934/jimo.2013.9.643
[8]	Ning Zhang. A symmetric Gauss-Seidel based method for a class of multi-period mean-variance portfolio selection problems. Journal of Industrial and Management Optimization, 2020, 16 (2) : 991-1008. doi: 10.3934/jimo.2018189
[9]	Xiaowei Chen, Qianlong Liu, Dan A. Ralescu. A bi-level optimization model for the asset-liability management of insurance companies. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022074
[10]	Zhongbao Zhou, Ximei Zeng, Helu Xiao, Tiantian Ren, Wenbin Liu. Multiperiod portfolio optimization for asset-liability management with quadratic transaction costs. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1493-1515. doi: 10.3934/jimo.2018106
[11]	Yu Yuan, Hui Mi. Robust optimal asset-liability management with penalization on ambiguity. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021121
[12]	Yingxu Tian, Junyi Guo, Zhongyang Sun. Optimal mean-variance reinsurance in a financial market with stochastic rate of return. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1887-1912. doi: 10.3934/jimo.2020051
[13]	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 and Management Optimization, 2016, 12 (4) : 1521-1533. doi: 10.3934/jimo.2016.12.1521
[14]	Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial and Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133
[15]	Hideaki Takagi. Extension of Littlewood's rule to the multi-period static revenue management model with standby customers. Journal of Industrial and Management Optimization, 2021, 17 (4) : 2181-2202. doi: 10.3934/jimo.2020064
[16]	Peng Zhang, Yongquan Zeng, Guotai Chi. Time-consistent multiperiod mean semivariance portfolio selection with the real constraints. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1663-1680. doi: 10.3934/jimo.2020039
[17]	Shan Liu, Hui Zhao, Ximin Rong. Time-consistent investment-reinsurance strategy with a defaultable security under ambiguous environment. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1185-1222. doi: 10.3934/jimo.2021015
[18]	Ishak Alia, Mohamed Sofiane Alia. Open-loop equilibrium strategy for mean-variance Portfolio selection with investment constraints in a non-Markovian regime-switching jump-diffusion model. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022048
[19]	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 and Management Optimization, 2022, 18 (2) : 1393-1423. doi: 10.3934/jimo.2021025
[20]	Qian Zhao, Yang Shen, Jiaqin Wei. Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1147-1171. doi: 10.3934/jimo.2020015

2021 Impact Factor: 1.411

Tools

Metrics

Tools

Article outline

Figures and Tables

2021 Impact Factor: 1.411

Tools

Figures and Tables

2021 Impact Factor: 1.411

American Institute of Mathematical Sciences

Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors