DUAL CHARACTERIZATION OF THE VALUE FUNCTION IN THE ROBUST UTILITY MAXIMIZATION PROBLEM

We consider the problem of maximizing the robust utility of terminal wealth in the framework of a market characterized only by the set of terminal wealths corresponding to all admissible strategies of an investor. Attention is mainly paid to the case where the utility function is finite on a half-line. We prove a minimax theorem which reduces the robust setting to a standard one, provide a dual characterization of the value function of the initial problem, and prove those properties of the solutions and the value functions of the initial and dual problems that do no require additional assumptions such as conditions on the asymptotic elasticity of the utility function.