Martingale Representation Theorem for the G-expectation

H. M. Soner, N. Touzi, J. Zhang

Published 2010-01-21, updated 2010-09-07Version 2

This paper considers the nonlinear theory of G-martingales as introduced by Peng. A martingale representation theorem for this theory is proved by using the techniques and the results established in an accompanying paper 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.