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

Qian Zhao, Rongming Wang, Jiaqin Wei*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1557-1585
Number of pages29
JournalJournal of Industrial and Management Optimization
Issue number4
Publication statusPublished - Oct 2016
Externally publishedYes


  • defined contribution pension fund
  • equilibrium strategies
  • extended HJB equation
  • non-exponential discounting
  • time-inconsistency


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