Abstract: This paper studies the optimal investment problem for defined-contribution (DC plan) with the death return and accidental return clauses. In the DC pension plan, the policyholder's contribution rate is determined, and the contribution rate and the investment income of the fund determine the amount of pension that the policyholder will receive in the future. The risk of this kind of pension insurance is entirely borne by the policyholder. Therefore, finding an optimal investment strategy is very important for guaranteeing the policyholder's pension. The insured may have accidents and deaths during the payment process. In order to protect their rights, a predetermined insurance premium should be refunded to the policyholder. The death return and accidental return are described by actuarial symbols and the compound Poisson process, respectively. And the Cram\'{e}r-Lundberg model is used to approximate the compound Poisson process. According to the mean-variance criterion we establish the corresponding Hamilton-Jacobi-Bellmen equations by stochastic control methods and obtain the time-consistent optimal investment strategy influenced by the death and accident of the policyholder. Finally, the effects of model parameters on the efficient frontier and value function are illustrated by numerical.

Key words: DC pension, mean-variance criterion, returns of death, returns of accident, optimal investment