Robust mean-variance efficient strategies of DC pension plans with ambiguity under stochastic interest rate and stochastic volatility

Abstract This paper studies a robust optimal investment problem with an ambiguity-averse manager (AAM) for a defined contribution (DC) plan with multiple risks under the mean-variance criterion. In the pension accumulation stage, the interest rate, the volatility and the salary level are considered to be stochastic. The financial market consists of a risk-free asset, a risky asset and a rolling bond. We assume that the term structure of interest rates is driven by an affine interest rate model, while the stock price and the salary level are modeled by the stochastic volatility model with stochastic interest rate. The goal of an AAM is to find a robust optimal strategy to maximize the expectation of terminal wealth and minimize the variance of terminal wealth in the worst-case scenario. By applying the Lagrange dual theory and the robust optimal control approach, we obtain closed-form expressions of the robust efficient strategy and the efficient frontier, and subsequently some special cases are derived. Finally, a numerical example is given to illustrate the results obtained. AMS classifications: 60H30, 91G10, 93E20.