Utility maximization: a dual problem and connections with upper prices of hedging contingent claims

In the first part of the talk we discuss the problem of maximizing robust utility from terminal wealth and its special cases. The main attention will be paid to a dual problem for a general static market model in the case where the utility function is finite on a half-line.
In the second part of the talk we discuss, in particular, for a general dynamic market model, necessary and sufficient conditions for a dual problem to be expressed in terms of supermartingale densities or measures. It turns out that this problem is closely related to the question whether the upper price of a contingent claim can be expressed in the same terms.