Equilibrium multi-period investment strategy for a DC pension plan with incomplete information: Hidden Markov model

In the financial market with both observable and unobservable market states, this article explores the equilibrium investment strategy for a DC pension plan with the mean-variance criterion in a discrete-time setting. The dynamics of the partially observed market state are described by a discrete-time finite-state hidden Markov chain. There is a riskless asset and a risky asset in the financial market, where the return rate of the risky asset depends both on the observable and unobservable market states. Meanwhile, the stochastic salary process is also modulated by the observable and unobservable market states. Under the framework of non cooperative game, we first define the equilibrium investment strategy for the multi-period mean-variance DC pension plan. By adopting the sufficient statistics method, the investment problem for the mean-variance DC pension plan with incomplete information is transformed into the one with complete information. The closed-form equilibrium investment strategy is derived by solving the extended Bellman equation. Finally, numerical results show that the incomplete information has significant impacts on the equilibrium investment strategy and the equilibrium efficient frontier. Neglecting the reality of incomplete information in the financial market will reduce the investment benefit of the DC pension plan. The longer the investment horizon, the greater the investment benefit loss for the DC pension plan.