Abstract

In reality, investors are uncertain about the dynamics of the risky asset returns. Therefore, investors prefer to make robust investment decisions. In this paper, we propose an α-robust utility maximization problem under uncertain parameters. The investor is allowed to invest in a financial market consisting of a risk-free asset and a risky asset. The uncertainty about the expected return rate is parameterized by a nonempty set. Different from most existing literature of robust utility maximization problem where investors are generally assumed to be extremely ambiguity-averse as they tend to only consider expected utility in the worst-case scenario, we pay attention to the investors who are not only ambiguity-averse but also ambiguity seeking. Under power utility, we provide the implicit function representations for the pre-committed strategy, equilibrium strategy of open-loop type and equilibrium strategy of closed-loop type. Some properties about the optimal trading strategies, the best-case and worst-case parameters under three different kinds of strategies are provided.