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...

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...