Time-consistent investment strategy for a DC pension plan with hidden Markov regime switching

Abstract

This paper studies the time-consistent investment strategy for a DC pension plan under a hidden Markov regime-switching economy. Assume that the stock return rate is related to the market state, which is described by an unobservable continuous-time, homogeneous Markov chain. In addition, the inflation risk and the stochastic salary are considered in our model. Firstly, the optimal investment problem for the DC plan under partial information is transformed into one under complete information by using the Wonham filtering theory. Then, by solving an extended HJB system of equations, the time-consistent investment strategy and corresponding value function are derived. Furthermore, we compare the time-consistent strategy under partial information with that under complete information and the suboptimal strategy when ignoring learning. Finally, the Monte Carlo method is used for sensitivity analysis and comparative analysis of different strategies, and the associated economic explanations are provided.