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In an incomplete market driven by time-changed L\'evy noises we consider theproblem of hedging a financial position coupled with the underlying risk ofmodel uncertainty. Then we study hedging under worst-case-scenario. Theproposed strategies are not necessarily self-financing and include theinterplay of a cost process to achieve the perfect hedge at the end of the timehorizon. The hedging problem is tackled in the framework of stochasticdifferential games and it is treated via backward stochastic differentialequations. Two different information flows are considered and the solutionscompared.

Hedging under worst-case-scenario in a market driven by time-changed L\'evy noises