Robust utility maximization with extremely ambiguity-loving and ambiguity-aversion preferences

In this paper, we investigate the robust utilitymaximization problems under both preferences of extremely ambiguity loving and ambiguity aversion. By a fundamental martingale characterization technique on nonlinear expectations, optimal investment strategies are explicitly solved in a general non- Markovian framework via backward stochastic differential equations. Different with previous works in the literature assuming the convexity of the set of prior probabilitymeasuresQ, our analysis are independent of the cardinality ofQ. Our results show that extremely ambiguity- loving ( resp. - aversion) investors will adopt the extremely aggressive ( resp. conservative) investment strategy.