Constructing sublinear expectations on path space

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G$G$-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G$G$-expectation, and an optional sampling theorem that holds without exceptional set. Our results also shed light on the inherent limitations to constructing sublinear expectations through aggregation.