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October  2016, 12(4): 1557-1585. doi: 10.3934/jimo.2016.12.1557

Time-inconsistent consumption-investment problem for a member in a defined contribution pension plan

 1 School of Business Information, Shanghai University of International Business and Economics, Shanghai 201620, China 2 School of Statistics and Research Centre of International Finance and Risk Management, East China Normal University, Shanghai 200241, China 3 School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai 200241, China

Received  October 2013 Revised  October 2015 Published  January 2016

In this paper, we investigate the consumption-investment problem for a member of the defined contribution pension plan with non-constant time preferences. The aim of the member is to maximize the discounted utility of the consumption. It leads to a time-inconsistent control problem in the sense that the Bellman optimality principle does no longer hold. In our model, the contribution rate is assumed to be a fixed proportion of the scheme member's salary, and the pension fund can be invested in a risk-free asset, an index bond and a stock whose return follows a geometric Brownian motion. Two utility functions are considered: the power utility and the logarithmic utility. We characterize the time-consistent equilibrium consumption-investment strategies and the value function in terms of a solution of an integral equation in both situations. The existence and uniqueness of the solution is verified and the approximation of the solution is obtained. We present some numerical results of the equilibrium consumption rate and equilibrium investment policy with three types of discount functions.
Citation: Qian Zhao, Rongming Wang, Jiaqin Wei. Time-inconsistent consumption-investment problem for a member in a defined contribution pension plan. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1557-1585. doi: 10.3934/jimo.2016.12.1557
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References:
 [1] Wei Zhong, Yongxia Zhao, Ping Chen. Equilibrium periodic dividend strategies with non-exponential discounting for spectrally positive Lévy processes. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020087 [2] Ishak Alia. A non-exponential discounting time-inconsistent stochastic optimal control problem for jump-diffusion. Mathematical Control & Related Fields, 2019, 9 (3) : 541-570. doi: 10.3934/mcrf.2019025 [3] Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumption-investment strategy with non-exponential discounting. Journal of Industrial & Management Optimization, 2020, 16 (1) : 207-230. doi: 10.3934/jimo.2018147 [4] Jingzhen Liu, Liyuan Lin, Ka Fai Cedric Yiu, Jiaqin Wei. Non-exponential discounting portfolio management with habit formation. Mathematical Control & Related Fields, 2020, 10 (4) : 761-783. doi: 10.3934/mcrf.2020019 [5] Jiongmin Yong. Time-inconsistent optimal control problems and the equilibrium HJB equation. Mathematical Control & Related Fields, 2012, 2 (3) : 271-329. doi: 10.3934/mcrf.2012.2.271 [6] Qian Zhao, Yang Shen, Jiaqin Wei. Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020015 [7] Chuangwei Lin, Li Zeng, Huiling Wu. Multi-period portfolio optimization in a defined contribution pension plan during the decumulation phase. Journal of Industrial & Management Optimization, 2019, 15 (1) : 401-427. doi: 10.3934/jimo.2018059 [8] Haiyang Wang, Zhen Wu. Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation. Mathematical Control & Related Fields, 2015, 5 (3) : 651-678. doi: 10.3934/mcrf.2015.5.651 [9] Jérôme Buzzi, Véronique Maume-Deschamps. Decay of correlations on towers with non-Hölder Jacobian and non-exponential return time. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 639-656. doi: 10.3934/dcds.2005.12.639 [10] Huiling Wu, Xiuguo Wang, Yuanyuan Liu, Li Zeng. Multi-period optimal investment choice post-retirement with inter-temporal restrictions in a defined contribution pension plan. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2857-2890. doi: 10.3934/jimo.2019084 [11] John A. D. Appleby, Alexandra Rodkina, Henri Schurz. Pathwise non-exponential decay rates of solutions of scalar nonlinear stochastic differential equations. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 667-696. doi: 10.3934/dcdsb.2006.6.667 [12] Xu Xu, Xin Zhao. Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model. Discrete & Continuous Dynamical Systems - A, 2020, 40 (8) : 4777-4800. doi: 10.3934/dcds.2020201 [13] Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 [14] Yanbin Tang, Ming Wang. A remark on exponential stability of time-delayed Burgers equation. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 219-225. doi: 10.3934/dcdsb.2009.12.219 [15] Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693 [16] Liyuan Wang, Zhiping Chen, Peng Yang. Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020018 [17] Baojun Bian, Shuntai Hu, Quan Yuan, Harry Zheng. Constrained viscosity solution to the HJB equation arising in perpetual American employee stock options pricing. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5413-5433. doi: 10.3934/dcds.2015.35.5413 [18] Qiang Yan, Mingqiao Luan, Yu Lin, Fangyu Ye. Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020106 [19] Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 [20] Sebastián Ferrer, Martin Lara. Families of canonical transformations by Hamilton-Jacobi-Poincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223-241. doi: 10.3934/jgm.2010.2.223

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