Robust optimal investment strategy for an AAM of DC pension plans with stochastic interest rate and stochastic volatility

In this paper, we investigate a robust optimal investment problem for an ambiguity-averse member (AAM) of defined contribution (DC) pension plans with stochastic interest rate and stochastic volatility. The AAM has access to a risk-free asset, a bond and a stock in a financial market. We assume that the interest rate is described by an affine model, which includes the Cox–Ingersoll–Ross model and the Vasicek model as special cases, while the stock price is driven by the Heston’s stochastic volatility model. Moreover, the AAM has different levels of ambiguity aversion about the diffusion parts of the interest rate and the stock’s price and volatility. She attempts to maximize the expected power utility of her terminal wealth under the worst-case scenario. By applying the stochastic dynamic programming approach, we derive a robust optimal investment strategy and the corresponding value function explicitly, and subsequently two special cases are discussed. Finally, a numerical example is presented to illustrate the impact of model parameters on the robust optimal investment strategy and to explain the economic meaning of our theoretical results. The numerical example shows that the AAM’s ambiguity aversion levels about the interest rate and the stock’s price and volatility have different impacts on the proportions invested in the risky assets, and that ignoring model uncertainty always incurs utility losses for the AAM.