Geodesic
Distributional uncertainty of the financial time series measured by $G$-expectation
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 914-928

Voir la notice de l'article provenant de la source Math-Net.Ru

Based on the law of large numbers and the 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 a 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.
Keywords: autoregressive model, sublinear expectation, volatility uncertainty, $G$-VaR, $G$-normal distribution. 
@article{TVP_2021_66_4_a13,
     author = {Shige Peng and Shuzhen Yang},
     title = {Distributional uncertainty of the financial time series measured by $G$-expectation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {914--928},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a13/}
}
TY  - JOUR
AU  - Shige Peng
AU  - Shuzhen Yang
TI  - Distributional uncertainty of the financial time series measured by $G$-expectation
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2021
SP  - 914
EP  - 928
VL  - 66
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a13/
LA  - ru
ID  - TVP_2021_66_4_a13
ER  - 
%0 Journal Article
%A Shige Peng
%A Shuzhen Yang
%T Distributional uncertainty of the financial time series measured by $G$-expectation
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2021
%P 914-928
%V 66
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a13/
%G ru
%F TVP_2021_66_4_a13
Shige Peng; Shuzhen Yang. Distributional uncertainty of the financial time series measured by $G$-expectation. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 4, pp. 914-928. http://geodesic.mathdoc.fr/item/TVP_2021_66_4_a13/