  In this paper the robust utility maximization problem for a market model
based on L\'evy processes is analyzed. The interplay between the form of the
utility function and the penalization function required to have a well posed
problem is studied, and for a large class of utility functions it is proved
that the dual problem is solvable as well as the existence of optimal
solutions. The class of equivalent local martingale measures is characterized
in terms of the parameters of the price process, and the connection with convex
risk measures is also presented.
