Before revision:  By using the stochastic control approach initiated in Galichon, Henry-Labord\`ere and Touzi, we identify the optimal hedging strategies and the corresponding prices in the one-marginal case .
After revision:  By using the stochastic control approach initiated in Galichon, Henry-Labord\`ere and Touzi, we identify the optimal hedging strategies , as well as the market models that realize the extremal no-arbitrage prices .