Girsanov's formula for G-Brownian motion

Abstract

In this paper, we establish Girsanov's formula for $G$-Brownian motion. Peng (2007, 2008) constructed $G$-Brownian motion on the space of continuous paths under a sublinear expectation called $G$-expectation; as obtained by Denis et al. (2011), $G$-expectation is represented as the supremum of linear expectations with respect to martingale measures of a certain class. Our argument is based on this representation with an enlargement of the associated class of martingale measures, and on Girsanov's formula for martingales in the classical stochastic analysis. The methodology differs from that of Xu et al. (2011), and applies to the multi-dimensional $G$-Brownian motion.

References in corpus (2)

• A variational representation and large deviations for functionals of G-Brownian motion
• A variational representation for G-Brownian functionals

Cited by in corpus (13)

• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion
• An $\alpha$-stable limit theorem under sublinear expectation
• Coherent Price Systems and Uncertainty-Neutral Valuation
• A variational representation and large deviations for functionals of G-Brownian motion
• Harnack Inequality and Gradient Estimate for $G$-SDEs with Degenerate Noise
• A variational representation for G-Brownian functionals
• A note on pricing of contingent claims under G-expectation
• Harnack Inequality and Applications for SDEs Driven by $G$-Brownian motion
• Martingale Problem under Nonlinear Expectations
• Girsanov formula for $G$-Brownian motion: the degenerate case
• Robust Mean-Variance Hedging via G-Expectation
• Harnack and log Harnack Inequalities for $G$-SDEs with Multiplicative Noise
• Robust valuation and risk measurement under model uncertainty