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

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 Kalman filter 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 effective frontier is derived. Finally, using the Monte Carlo method to perform numerical simulations, we analyze the effects of partial information and premium return clauses on the stock investment ratio and effective frontier, and give corresponding economic explanations.