Model independent bound for option pricing: a stochastic control aproach

This problem is classically addressed by the so-called Skorohod Embedding problem. We instead develop a stochastic control approach. Unlike the previous literature, our formulation seeks the optimal no arbitrage bounds given the knowledge of the distribution at some (or various) point in time. This problem is converted into a classical stochastic control problem by means of convex duality. We obtain a general characterization, and provide explicit optimal bounds in some examples beyond the known classical ones. In particular, we solve completely the case of finitely many given marginals.