Before revision:  Probabilistic dual representations are obtained for the bid and ask pricesof such options, together with constructions of hedging strategies , optimal stopping times and approximate martingale representations for both long and short option positions  .
After revision:  Probabilistic dual representations are obtained for the bid and ask pricesof such options, together with constructions of hedging strategies , optimal stopping times and approximate martingale representations for both long and short option positions in this setting, together with probabilistic (martingale) representations for the option prices .