Optimal Investment Strategy for a Robust DC Pension Plan under the Heston Model

We consider an optimal robust investment problem for a defined contribution DC pension plan with stochastic income and model uncertainty. In the model, the pension account is allowed to invest into a risky asset and a risk-free asset, and the dynamic of the price of risky asset follows a Heston model. The objective of the problem is to maximize the expected utility of the terminal relative wealth by choosing admissible investment strategies. By using the stochastic control dynamic programming approach, we find the robust optimal investment strategy and the corresponding value function when the utility function has the power or the exponential form, respectively. At last, we show a numerical example to further analyze the theoretical results through the MATLAB software.