Optimal Time-Consistent Investment Strategy for a DC Pension Plan with the Return of Premiums Clauses and Annuity Contracts

Defined contribution and annuity contract are merged into one pension plan to study both accumulation phase and distribution phase, which results in such effects that both phases before and after retirement being "defined". Under the Heston's stochastic volatility model, this paper focuses on mean-variance insurers with the return of premiums clauses to study the optimal time-consistent investment strategy for the DC pension merged with an annuity contract. Both accumulation phase before retirement and distribution phase after retirement are studied. In the time-consistent framework, the extended Hamilton-Jacobi-Bellman equations associated with the optimization problem are established. Applying stochastic optimal control technique, the time-consistent explicit solutions of the optimal strategies and the efficient frontiers are obtained. In addition, numerical analysis illustrates our results and also deepens our knowledge or understanding of the research results.