Martingale representation theorem for the -expectation

This paper considers the nonlinear theory of G -martingales as introduced by Peng (2007) in [16,17]. 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 problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.