Time-consistent multi-period investment strategy for a DC pension plan with inflation risk, salary risk and a return of premiums clause

An optimal investment problem for a defined contribution (DC) pension plan during the accumulation phase is studied under the discrete-time mean–variance framework in this paper. To protect the rights of pension members who die before retirement, a return of premiums clause is introduced, under which a member who dies before retirement can withdraw all the premiums he/she has contributed. Unlike previous studies (Bian et al., 2018; He & Liang, 2013) on the DC pension funds investment problem with the premium return clause, where they set the contribution of pension members as a constant, which is inconsistent with the investment reality, this paper assumes that the contribution of pension members is a proportion of stochastic salary. We assume that the financial market consists of one risk-free asset and multiple risky assets. Since the time horizon of the pension plan is generally very long, we consider the impact of the inflation risk. We regard this problem as a non-cooperative game whose equilibrium strategy is a time-consistent strategy, and derive the analytical expressions for the equilibrium strategy, the equilibrium value function and the equilibrium efficient frontier by using the extended Bellman equation and the matrix representation technique. Moreover, some special cases of our model are discussed. Finally, some numerical examples based on real data from the Chinese market are provided to shed light on the theoretical results established in this paper.