Robust optimal investment strategy of DC pension plans with stochastic salary and a return of premiums clause

In this paper, we investigate a robust optimal investment problem for a defined contribution (DC) pension plan with a return of premiums clause, taking account of the inflation risk and the salary risk. The members in the pension plan continuously contribute a fixed proportion of their stochastic salaries into the pension fund and receive the benefits at retirement time. Due to a return of premiums clause, the members who die in the accumulation phase have the right to withdraw their accumulated premiums. The pension fund manager can invest the wealth of the fund into a financial market consisting of a risk-free asset, an inflation-indexed bond and a stock. The manager is assumed to be ambiguity-averse and attempt to maximize the expected utility of the terminal wealth in each alive member's pension account under the worst-case scenario. By adopting a new state variable which represents the accumulated premiums and using dynamic programming approach, we derive the robust optimal investment strategy and the corresponding value function. Finally, the effects of the stochastic salary, the return of premiums clause and the attitude about the model uncertainty on the robust optimal investment strategy are illustrated by mathematical and numerical analysis.