  Based on law of large numbers and central limit theorem under nonlinear
expectation, we introduce a new method of using G-normal distribution to
measure financial risks. Applying max-mean estimators and small windows method,
we establish autoregressive models to determine the parameters of G-normal
distribution, i.e., the return, maximal and minimal volatilities of the time
series. Utilizing the value at risk (VaR) predictor model under G-normal
distribution, we show that the G-VaR model gives an excellent performance in
predicting the VaR for a benchmark dataset comparing to many well-known VaR
predictors.

Mathematical Finance