G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

Understand

We introduce a new notion of G-normal distributions.

• This will bring us to a new framework of stochastic calculus of Ito's type (Ito's integral, Ito's formula, Ito's equation) through the corresponding G-Brownian motion.
• We will also present analytical calculations and some new statistical methods with application to risk analysis in finance under volatility uncertainty.
• Our basic point of view is: sublinear expectation theory is very like its special situation of linear expectation in the classical probability theory.