Time-consistent investment strategy for a DC pension plan with the return of premiums clause and mispricing
研究了均值-方差准则下，具有保费返还条款和错误定价的固定缴费养老金计划的时间一致投资策略，推导出显式解并发现保费利率、错误定价和流动性对投资比例的影响。
This paper investigates the time-consistent investment strategy for a defined-contribution (DC) pension plan with the return of premiums clause and mispricing under the mean-variance criterion. During the accumulation phase, the members of the DC pension plan contribute a fixed proportion of their stochastic income into the DC pension account as premiums. The investment opportunity set consists of a market index, a risk-free asset and a pair of mispriced stocks. The dynamics for the expected return rate of the mispriced stocks and the mispricing feature are described by mean-reverting stochastic processes. Moreover, if the DC pension plan members die during the accumulation phase, their beneficiaries are allowed to withdraw the accumulated premiums at a predetermined interest rate, that is, a return of premiums clause is introduced. Under a game theoretic framework, the explicit expressions of the time-consistent investment strategy and the corresponding value function are derived. Numerical examples are presented to illustrate our derived results. Some key findings include: (i) as the growth of the predetermined interest rate accumulated by the premiums, the proportion invested in the market index rises; (ii) larger mispricing increases the portfolio's absolute positions in each stock; (iii) under the given expected terminal wealth, strong market liquidity significantly reduces the investment risk for the DC pension plan.