Robust Optimal Investment in Discrete Time for Unbounded Utility   Function
  This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line. 
Laurence Carassus, Romain Blanchard
q-fin.MF