部分信息下带有保费返还条款的DC养老金时间一致性投资策略

Time Consistent Investment Strategy of DC Pension with Premium Return Clause under Partial Information

本文研究了部分信息下带有保费返还条款的DC养老金的时间一致性投资策略.假设养老金管理者只拥有股票的部分信息,即只能观测到股票的价格,而不能观测到股票的收益率.养老金带有保费返还条款,在基金累积期死亡的参与者可以获得前期缴纳的所有保费.此外,本文还考虑了通胀风险以及随机工资.首先,利用卡尔曼滤波理论,将部分信息情形下的最优投资组合问题转化为一个完全信息情形下的问题.然后,通过求解一个扩展的HJB方程,得到时间一致性投资策略和最优值函数,并给出了均值–方差有效前沿的参数表达式.最后,用蒙特卡洛方法进行数值模拟,分析了部分信息和保费返还条款对股票投资比例和有效前沿的影响,并给出了相应的经济学解释.

This paper studies the time-consistent investment strategy of DC pensions with premium return clauses under partial information.We assume that pension managers only have partial information about stock,that is,they can only observe the price of the stock,but not the rate of return of the stock.The pension has a premium return clause.If the insured person dies during the fund accumulation period,the premium paid by him needs to be refunded.In addition,this article also considers inflation and random wages.First,using the Kalmanfilter theory,the optimal portfolio problem under the partial information situation is transformed into a problem under the complete information situation.Then,by solving an extended HJB equation,the time-consistent investment strategy and the optimal value function are obtained,and a parametric formula of the mean-variance eective frontier is derived.Finally,using the Monte Carlo method to perform numerical simulations,we analyze the eects of partial information and premium return clauses on the stock investment ratio and eective frontier,and give corresponding economic explanations.