Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income

doi:10.1007/s40305-021-00386-1

Journal of the Operations Research Society of China ›› 2022, Vol. 10 ›› Issue (3): 559-577.doi: 10.1007/s40305-021-00386-1

收稿日期:2021-06-18 修回日期:2021-11-01 出版日期:2022-09-30 发布日期:2022-09-06

Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income

Li-Hua Bian¹, Xing-Yi Li², Zhong-Fei Li³

1. School of Mathematics and Statistics, Xuzhou Institute of Technology, Xuzhou 221000, Jiangsu, China;
2. School of Business, Sun Yat-sen University, Guangzhou 510275, Guangdong, China;
3. Department of Finance, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China

Received:2021-06-18 Revised:2021-11-01 Online:2022-09-30 Published:2022-09-06
Contact: Zhong-Fei Li,Li-Hua Bian,Xing-Yi Li E-mail:lnslzf@mail.sysu.edu.cn;bianlh1028@163.com;lixy399@mail2.sysu.edu.cn
Supported by:
This paper is supported by the National Natural Science Foundation of China (Nos.71991474,71721001 and 72001219).

摘要/Abstract

Abstract: This paper studies two multi-period mean-variance investment problems for a DC pension member before and after retirement.At any time,the pension manager can invest in a risk-free asset and multi-risky assets.Before retirement,the manager tries to optimize the mean-variance utility of the wealth in the member's pension account at retirement.At retirement,the pension account wealth (or part of it) is used to purchase a paid-up annuity.After retirement,the manager has to pay the guaranteed annuity,continues to invest,and aims to optimize the mean-variance utility of the terminal wealth at a fix future time,to satisfy the pension member's heritage and life needs in the next stage.Interest rate risk and income risk are introduced.Applying the game theory and the extended Bellman equation,the time-consistent investment strategies and the efficient frontiers before and after retirement are obtained explicitly.Obtained results indicate that the stochastic interest rate and the stochastic income have essential effects on the investment strategies.

Key words: DC pension fund, Time-consistent strategy, Stochastic income, Stochastic interest rate, Multi-period mean-variance model

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2022, 10(3): 559-577.

Li-Hua Bian, Xing-Yi Li, Zhong-Fei Li. Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income[J]. Journal of the Operations Research Society of China, 2022, 10(3): 559-577.

参考文献

[1] Deelstra, G., Grasselli, M., Koehl, P.F.:Optimal investment strategies in the presence of a minimum guarantee. Insur. Math. Econ. 33, 189-207(2003)
[2] Gao, J.W.:Stochastic optimal control of DC pension funds. Insur. Math. Econ. 42, 1159-1164(2008)
[3] Guan, G.H., Liang, Z.H.:Optimal management of DC pension plan in a stochastic interest rate and stochastic volatility framework. Insur. Math. Econ. 57, 58-66(2014)
[4] Guan, G.H., Liang, Z.X.:Optimal management of DC pension plan under loss aversion and value-atRisk constraints. Insur. Math. Econ. 69, 224-237(2016)
[5] Bian, L.H., Li, Z.F., Yao, H.X.:Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause. Insur. Math. Econ. 81, 78-94(2018)
[6] Wu, H.L., Zeng, Y.:Equilibrium investment strategy for defined-contribution pension schemes with generalized mean-variance criterion and mortality risk. Insur. Math. Econ. 64, 396-408(2015)
[7] Yao, H.X., Lai, Y.Z., Ma, Q.H., Jian, M.J.:Asset allocation for a DC pension fund with stochastic income and mortality risk:a multi-period mean-variance framework. Insur. Math. Econ. 54, 84-92(2014)
[8] Yao, H.X., Chen, P., Li, X.:Multi-period defined contribution pension funds investment management with regime-switching and mortality risk. Insur. Math. Econ. 71, 103-113(2016)
[9] Zhang, L., Zhang, H., Yao, H.X.:Optimal investment management for a defined contribution pension fund under imperfect information. Insur. Math. Econ. 79, 210-224(2018)
[10] Markowitz, H.:Portfolio selection. J. Finance 7(1), 77-91(1952)
[11] Li, D., Ng, W.L.:Optimal dynamic portfolio selection:multiperiod mean-variance formulation. Math. Finance 10, 387-406(2000)
[12] Zhou, X.Y., Li, D.:Continuous-time mean-variance portfolio selection:a stochastic LQ framework. Appl. Math. Optim. 42(1), 19-33(2000)
[13] Menoncin, F., Vigna, E.:Mean-variance target-based optimisation in DC plan with stochastic interest rate. In:Carlo Alberto Notebooks, No. 337. Collegio Carlo Alberto (2013)
[14] Guan, G.H., Liang, Z.X.:Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns. Insur. Math. Econ. 61, 99-109(2015)
[15] Højgaard, B., Vigna, E.:Mean-variance portfolio selection and efficient frontier for defined contribution pension schemes. http://vbn.aau.dk/files/11498557/R-2007-13.pdf (2007)
[16] Vigna, E.:On efficiency of mean-variance based portfolio selection in defined contribution pension schemes. Quant. Financ. 14, 237-258(2014)
[17] Basak,S.,Chabakauri,G.:Dynamicmean-varianceassetallocation.Rev.Financ.Stud. 23,2970-3016(2010)
[18] Björk, T., Murgoci, A.:A general theory of Markovian time inconsistent stochastic control problem. Working paper. http://ssrn.com/abstract=1694759(2010)
[19] Wu, H.L., Zhang, L., Chen, H.:Nash equilibrium strategies for a defined contribution pension management. Insur. Math. Econ. 62, 202-214(2015)
[20] Li,D.P.,Rong,X.M.,Zhao,H.:Time-consistentinvestmentstrategyforDCpensionplanwithstochastic salary under CEV model. J. Syst. Sci. Complex. 29, 428-454(2016)
[21] Yao, H.X., Li, Z.F., Li, D.:Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability. Eur. J. Oper. Res. 252(3), 837-851(2016)
[22] Devolder, P., Princep, M.B., Fabian, I.D.:Stochastic optimal control of annuity contracts. Insur. Math. Econ. 33, 227-238(2003)
[23] Gao, J.W.:Optimal portfolios for DC pension plans under a CEV model. Insur. Math. Econ. 44(3), 479-490(2009)
[24] Bian, L.H., Li, Z.F., Yao, H.X.:Time-consistent strategy for a multi-period mean-variance assetliability management problem with stochastic interest rate. J. Indus. Manag. Optim. 17(3), 1383-1410(2020)
[25] Wu, H.L., Chen, H.:Nash equilibrium strategy for a multi-period mean-variance portfolio selection problem with regime switching. Econ. Modell. 46, 79-90(2015)

Time-Consistent Investment Strategies for a DC Pension Member with Stochastic Interest Rate and Stochastic Income

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价