带有死亡和意外返还条款的DC型养老金的最优投资问题

本文研究带有死亡返还和意外返还条款的确定缴费型养老金的最优投资问题．在确定缴费型养老金计划中，投保人的缴费率是确定的，投保人未来获得的养老金数额由缴费率和基金的投资收益决定．这种养老保险的风险完全由投保人承担，因此寻找最优投资策略对于保证投保人的退休给付有重要意义．投保人在缴费过程中可能会出现意外和死亡的情况，为了保障其权益，应该给投保人返还一定的保费．死亡返还和意外返还分别使用精算符号和复合泊松过程来描述，并利用Cram'{e}r-Lundberg模型对复合泊松过程进行了近似．根据均值--方差目标采用随机控制的方法，建立相应的Hamilton-Jacobi-Bellman方程并求解，得到受死亡和意外影响的确定缴费型养老金的时间一致最优策略，最后数值分析模型中各参数对有效边界和价值函数的影响．

Optimal Investment Problem for DC Pension Plan with Return of Death and Accident Clauses

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.