Robust pricing-hedging duality for multi-action options

We aim to generalize the duality results of arXiv:1604.05517v2 to the case of exotic options that allow the buyer to choose some action from an action space, countable or uncountable, at each time step in the setup of arXiv:1305.6008v3. By introducing an enlarged canonical space, we reformulate the superhedging problem for such exotic options as a problem for European options. Then in a discrete time market with the presence of finitely many statically traded liquid options, we prove the pricing-hedging duality for such exotic options as well as the European pricing-hedging duality in the enlarged space.