Super-replication on illiquid markets—semistatic approach

We investigate the pricing-hedging duality for path dependent European options under model uncertainty in discrete time. The super-replicating portfolio consists of a dynamically traded illiquid risky stock and a static position in vanilla options which can be exercised at maturity. We provide the minimal super-replication price as the supremum of penalized expectations of the payoff over all probability measures which are consistent with observed market prices.