Supermartingale Decomposition Theorem under G-expectation

Abstract

The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown that this kind of supermartingales have the decomposition similar to the classical case. The main ideas are to apply the uniformly continuous property of $S_G^{\beta }(0,T)$, the representation of the solution to $G$-BSDE and the approximation method via penalization.

References in corpus (4)

• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• Dynamically Consistent Nonlinear Evaluations and Expectations
• Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion

Cited by in corpus (3)

• Reflected Solutions of BSDEs Driven by G-Brownian Motion
• Multi-dimensional reflected BSDEs driven by $G$-Brownian motion with diagonal generators
• Exit times for semimartingales under nonlinear expectation