Martingale Representation Theorem for the G-expectation

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.

References in corpus (5)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Some properties on $G$-evaluation and its applications to $G$-martingale decomposition
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Dual formulation of second order target problems
• Random G-expectations

Cited by in corpus (41)

• Arbitrage and duality in nondominated discrete-time models
• Some properties on $G$-evaluation and its applications to $G$-martingale decomposition
• Dual formulation of second order target problems
• Random G-expectations
• On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients
• Pathwise Construction of Stochastic Integrals
• Note on Viscosity Solution of Path-Dependent PDE and G-Martingales
• Girsanov's formula for G-Brownian motion
• Exponential Stability of Solutions to Stochastic Differential Equations Driven by G-Levy Process
• Sublinear Expectations and Martingales in discrete time
• Supermartingale Decomposition Theorem under G-expectation
• BSDEs driven by $G$-Brownian motion with uniformly continuous generators
• An $\alpha$-stable limit theorem under sublinear expectation
• Financial markets with volatility uncertainty
• Reduced-form framework under model uncertainty
• Wellposedness of Second Order Backward SDEs
• Zero-sum path-dependent stochastic differential games in weak formulation
• A New Result for Second Order BSDEs with Quadratic Growth and its Applications
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• On the Hedging of Options On Exploding Exchange Rates
• Some Norm Estimates for Semimartingales
• Quadratic backward stochastic differential equations driven by $G$-Brownian motion: discrete solutions and approximation
• Multiple G-Itô integral in the G-expectation space
• Stochastic optimal control problem with infinite horizon driven by G-Brownian motion
• Second Order Backward Stochastic Differential Equations with Quadratic Growth
• Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Some sample path properties of G-Brownian motion
• Partial Uncertainty and Applications to Risk-Averse Valuation
• Distributional Robust Kelly Gambling: Optimal Strategy under Uncertainty in the Long-Run
• Utility Maximization under Model Uncertainty in Discrete Time
• Minimal supersolutions of BSDEs under volatility uncertainty
• Stability theorems for stochastic differential equations driven by G-Brownian motion
• Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces
• Robust Mean-Variance Hedging via G-Expectation
• Robust Financial Bubbles
• Exit times for semimartingales under nonlinear expectation
• The Value of Insider Information for Super--Replication with Quadratic Transaction Costs
• Robust valuation and risk measurement under model uncertainty
• Doob's optional sampling and maximal inequality for $G$-martingales
• Ambiguous volatility and asset pricing in continuous time
• A weighted central limit theorem under sublinear expectations