具有保费退还条款的DC养老金最优投资研究

Optimal investment strategy for the DC plan with the return of premiums

本文研究具有保费退还条款的确定缴费型养老金个人账户的时间一致最优投资策略.假设养老金保费具有退还条款,需退还退休前死亡的参与者所缴的保费,账户由投资所产生的利润将平均分给其他参与者.养老金可投资于无风险资产和服从跳-扩散过程的风险资产,在均值-方差目标下,建立相应问题的广义Hamilton-Jacobi-Bellman(HJB)方程,利用博弈论,最优控制等方法,得到时间一致的最优投资策略和最优值函数.数值分析跳-扩散模型中各参数对均衡策略和最优值函数的影响.利用Monte Carlo方法,比较具有保费退还条款与没有退还条款时的最优策略变化.

This paper studies the time-consistent investment strategy in the DC plan during tim accmnu- lation phase. Most of DC plan have return of premium clauses, which means the members withdraw their premiums when they die before retirement and the difference between the premium and accumulation is distributed to other members equally. Meanwhile, there are a risk-free asset and a risky asset whose price is modeled by jump-diffusion process. In the time-consistent framework, an extended Hamilton-Jacobi- Bellman （HJB） equations of the equilibrium value function is established. The closed-form expression for the time-consistent investment strategy and optimal value function are derived by stochastic control tech- nique. Moreover, the effects of jump-diffusion process on the equilibrium strategy and equilibrinm wflue function are illustrated by mathematical and numerical analysis. The differences of optimal strategies between plan with and without the return of premium are explored via Monte Carlo methods.