  We establish the existence of minimizers in a rather general setting of
dynamic stochastic optimization without assuming either convexity or coercivity
of the objective function. We apply this to prove the existence of optimal
portfolios for non-concave utility maximization problems in financial market
models with frictions (such as illiquidity), a first result of its kind. The
proofs are based on the dynamic programming principle whose validity is
established under quite general assumptions.
