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

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.