Robust utility maximization with proportional transaction costs

The existence of solutions of the robust utility maximization problem under proportional transaction costs is discussed. Utility functions are defined either on R+ or on R, risky asset prices have continuous trajectories and... [ view full abstract ]

The existence of solutions of the robust utility maximization problem under proportional transaction costs is discussed. Utility functions are defined either on R+ or on R, risky asset prices have continuous trajectories and admit consistent price systems. Our model assumes that there is a parametrization for the dynamics of risky assets. The primal problem is studied directly. More precisely, we introduce an appropriate topological space for finite variation processes and then study convex compactness of certain sets in this space. We furthermore rely on a recent convex compactness result of Delbaen and Owari in Orlicz spaces.