A Complete Representation Theorem for $G$-martingales

Abstract

In this paper we establish a complete representation theorem for $G$-martingales. Unlike the existing results in the literature, we provide the existence and uniqueness of the second order term, which corresponds to the second order derivative in Markovian case. The main ingredient of the paper is a new norm for that second order term, which is based on an operator introduced by Song [26].

22 pages

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• Optimal Stopping under Nonlinear Expectation
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• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion
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• Path Independence of Additive Functionals for SDEs under G-framework
• G-Expectation Weighted Sobolev Spaces, Backward SDE and Path Dependent PDE
• A stochastic recursive optimal control problem under the G-expectation framework
• A note on pricing of contingent claims under G-expectation
• Second Order Backward Stochastic Differential Equations with Quadratic Growth
• Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Martingale Problem under Nonlinear Expectations
• Some apriori estimates of G-BSDEs and the G-martingale representation for a special case
• Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty