  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.
