# American Institute of Mathematical Sciences

• Previous Article
Piecewise observers of rectangular discrete fuzzy descriptor systems with multiple time-varying delays
• JIMO Home
• This Issue
• Next Article
Optimal rebate strategies in a two-echelon supply chain with nonlinear and linear multiplicative demands
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
##### References:

show all references

##### References:
 [1] 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 [2] Jiaqin Wei, Danping Li, Yan Zeng. Robust optimal consumption-investment strategy with non-exponential discounting. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-24. doi: 10.3934/jimo.2018147 [3] 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 [4] 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 [5] 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 [6] 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 [7] 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, 2017, 13 (5) : 1-34. doi: 10.3934/jimo.2019084 [8] 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 [9] 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 [10] 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 [11] 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 [12] 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 [13] 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 [14] 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 [15] Manuel de León, Juan Carlos Marrero, David Martín de Diego. Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics. Journal of Geometric Mechanics, 2010, 2 (2) : 159-198. doi: 10.3934/jgm.2010.2.159 [16] Thierry Horsin, Peter I. Kogut. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result. Mathematical Control & Related Fields, 2015, 5 (1) : 73-96. doi: 10.3934/mcrf.2015.5.73 [17] Shouming Zhou, Chunlai Mu, Yongsheng Mi, Fuchen Zhang. Blow-up for a non-local diffusion equation with exponential reaction term and Neumann boundary condition. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2935-2946. doi: 10.3934/cpaa.2013.12.2935 [18] 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 [19] Yaru Xie, Genqi Xu. Exponential stability of 1-d wave equation with the boundary time delay based on the interior control. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 557-579. doi: 10.3934/dcdss.2017028 [20] Felipe Rivero. Time dependent perturbation in a non-autonomous non-classical parabolic equation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 209-221. doi: 10.3934/dcdsb.2013.18.209

2018 Impact Factor: 1.025