Martingale Representation Theorem for the G-expectation

TL;DR

This paper proves a martingale representation theorem within the nonlinear G-expectation framework, enabling hedging strategies in markets with uncertain volatility by leveraging second order stochastic calculus techniques.

Contribution

It introduces a martingale representation theorem for G-martingales, advancing the mathematical foundation for modeling and hedging under volatility uncertainty.

Findings

Established a martingale representation theorem for G-martingales.

Connected the theorem to hedging strategies in uncertain markets.

Utilized second order stochastic target problems and BSDEs.

Abstract

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.