Duality theory for optimal investments under model uncertainty

We extend the results of Kramkov and Schachermayer to the problem of robust utility maximization in an incomplete market setting. The robust utility functionals we are considering arise as numerical representations of investor preferences when the investor is uncertain about the correct probabilistic model and averse against both risk and model uncertainty. The usual approach is to reduce the problem to a standard problem under a least favorable model. An interesting feature of incomplete market models is that the least favorable model may admit arbitrage oportunities.