Abstract:

In this paper, we consider a time-consistent investment strategy for DC pension plan with a return of premiums clause and mispricing under the mean-variance criterion. We assume that the pension plan manager is allowed to invest the wealth in the pension account in a financial market consisting of a risk-free asset, a pair of mispriced stocks, and a market index following a $4/2$ stochastic volatility model. Under the framework of game theory, the explicit expressions of the time-consistent equilibrium investment strategy and the equilibrium efficient frontier are obtained by using stochastic control methods and solving the extended HJB system. Finally, the effects of risk aversion coefficient, mispricing and return of premiums clauses on equilibrium strategy and efficient frontier are illustrated by numerical simulations.

Key words: Defined contribution pension plan, Mean-variance criterion, $4/2$ stochastic volatility model, Return of premiums clauses, Mispricing, Equilibrium strategy