  In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g
processes, this paper characterizes superhedging prices, absence of arbitrage,
and utility maximizing strategies, under general frictions that make execution
prices arbitrarily unfavorable for high trading intensity. Such frictions
induce a duality between feasible trading strategies and shadow execution
prices with a martingale measure. Utility maximizing strategies exist even if
arbitrage is present, because it is not scalable at will.
