Before revision:  While typically the (random) constraint set is  neither closed nor convex , in several important cases of interest, the constraint is non-binding. In these instances, we explicitly identify optimal demands for derivative contracts, and state three notions of an arbitrage free price . Due to price impact, even if a price is not arbitrage free, the resulting arbitrage opportunity only exists for limited position sizes, and might be ignored because of hedging considerations.
After revision:  While typically the (random) constraint set is neither closed nor convex . Regarding hedging, non-linear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and might be ignored because of hedging considerations.