ROBUST OPTIMAL STRATEGIES OF DC PENSION PLANS WITH STOCHASTIC VOLATILITY AND STOCHASTIC INCOME UNDER MEAN-VARIANCE CRITERIA

Abstract

This paper studies a robust optimal investment problem under the mean-variance criterion for a defined contribution (DC) pension plan with an ambiguity-averse member (AAM), who worries about model misspecification and aims to find robust optimal strategy. The member has access to a risk-free asset (i.e., cash or bank account) and a risky asset (i.e., the stock) in a financial market. In order to get closer to the actual environment, we assume that both the income level and stock price are driven by Heston's stochastic volatility model. A continuous-time mean-variance model with ambiguity aversion for a DC pension plan is established. By using the Lagrangian multiplier method and stochastic optimal control theory, the closed-form expressions for robust efficient strategy and efficient frontier are derived. In addition, some special cases are derived in detail. Finally, a numerical example is presented to illustrate the effects of model parameters on the robust efficient strategy and the efficient frontier, and some economic implications have been revealed