In robust approach, instead of choosing one model, one considers superhedging simultaneously under a family of models, or pathwise on the set of feasible trajectories. Usually in the literature the focus is on the natural filtration $\mathbb F$ of the price process. Here we extend that to a general filtration $\mathbb G$ including the natural filtration of the price process $\mathbb F\subset \mathbb G$. Two filtrations can model asymmetry of information on the market.

We consider the price process as a canonical process on some restriction of space of $\mathbb R^d$-valued continuous functions on $[0, T]$. Price process represents underlying stocks and continuously traded options. Beside that we allow static position in options from a given set with given prices. One may look at the superhedging prices for an informed agent or at the market model prices induced by appropriate sets of martingale measures.

Our main result is showing that the pricing-hedging duality holds for the informed agent for some class of payoffs, in a number of interesting cases.

This is a joint work with Zhaoxu Hou and Jan Oblój.