We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng’s G-expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G-expectation. This can be seen as a Donsker-type result for the G-Brownian...

Given a càdlàg process X on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let Psem be the set of all probability measures P under which X is a semimartingale. We...

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an...

This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16] and [17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target...