Robust Utility Maximization in Discrete-Time Markets with Friction
  We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of financial markets. As a corollary, we obtain existence of an utility maximizer in the frictionless market model, markets with proportional transaction costs and also more general convex costs, like in the case of market impact. 
Ariel Neufeld, Mario Sikic
q-fin.MF math.OC math.PR