  In this paper we derive robust super- and subhedging dualities for contingent
claims that can depend on several underlying assets. In addition to strict
super- and subhedging, we also consider relaxed versions which, instead of
eliminating the shortfall risk completely, aim to reduce it to an acceptable
level. This yields robust price bounds with tighter spreads. As examples we
study strict super- and subhedging with general convex transaction costs and
trading constraints as well as risk-based hedging with respect to robust
versions of the average value at risk and entropic risk measure. Our approach
is based on representation results for increasing convex functionals and allows
for general financial market structures. As a side result it yields a robust
version of the fundamental theorem of asset pricing.
