Equilibrium investment strategy for a DC pension plan with learning about stock return predictability

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.