Time-consistent investment strategy for a DC pension plan with the return of premiums clause and mispricing

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.