  We consider dynamic sublinear expectations (i.e., time-consistent coherent
risk measures) whose scenario sets consist of singular measures corresponding
to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear
martingale which is also the value process of a superhedging problem. The
superhedging strategy is obtained from a representation similar to the optional
decomposition. Furthermore, we prove an optional sampling theorem for the
nonlinear martingale and characterize it as the solution of a second order
backward SDE. The uniqueness of dynamic extensions of static sublinear
expectations is also studied.
