On the Representation Theorem of G-Expectations and Paths of G--Brownian Motion

Abstract

We give a very simple and elementary proof of the existence of a weakly compact family of probability measures $\{P_{\theta }:\theta \in \Theta \}$ to represent an important sublinear expectation--G-expectation $\mathbb{E}[\cdot ]$. We also give a concrete approximation of a bounded continuous function $X(\omega )$ by an increasing sequence of cylinder functions $L_{ip}(\Omega )$ in order to prove that $C_b(\Omega )$ belongs to the $\mathbb{E}[|\cdot |]$-completion of the $L_{ip}(\Omega )$.

12 pages

References in corpus (3)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• A New Central Limit Theorem under Sublinear Expectations
• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

Cited by in corpus (1)

• Representation of G-martingales as stochastic integrals with respect to the G-Brownian motion