This paper investigates a time-consistent investment strategy under the mean-variance criterion for an investor who accumulates retirement savings through a defined contribution (DC) pension plan with stock and bond investment opportunities. The expected return rate on the stock is modulated by an unobservable predictor which follows a mean-reverting stochastic process. The evolution of the instantaneous interest rate is described by the Vasicek model. In addition, the contribution rate of the DC pension plan is stochastic and correlated with financial risks coming from the stochastic interest rate and stock price. In a game theoretic framework, we derive a closed-form equilibrium investment strategy and corresponding equilibrium value function for the mean-variance criterion by adopting the filtering technique and the stochastic control method. Furthermore, we provide an equilibrium investment strategy and equilibrium value function when the expected return rate of the stock is completely observable. Finally, some numerical examples are presented to demonstrate the sensitivity analysis of the equilibrium investment strategy and equilibrium efficient frontier. Numerical analysis confirms that there is non-negligible information loss on the equilibrium investment strategy and equilibrium value function due to partial observation in the stock price dynamics.

本文研究了在均值方差标准下的时间一致性投资策略，该策略通过具有股票和债券投资机会的固定缴款 (DC) 养老金计划积累退休储蓄的投资者。股票的预期回报率由一个不可观察的预测器调制，该预测器遵循均值回归随机过程。Vasicek 模型描述了瞬时利率的演变。此外，DC养老金计划的缴费率是随机的，与随机利率和股票价格带来的金融风险相关。在博弈论框架中，我们采用滤波技术和随机控制方法，推导出封闭式均衡投资策略和均值方差准则对应的均衡价值函数。此外，当股票的预期收益率完全可观察时，我们提供了均衡投资策略和均衡价值函数。最后，给出了一些数值例子来说明均衡投资策略和均衡有效边界的敏感性分析。数值分析证实，由于对股价动态的局部观察，均衡投资策略和均衡价值函数存在不可忽略的信息损失。