Exact penalty functions in constrained optimization
SIAM Journal on Control and Optimization
Journal of Multivariate Analysis
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Using a bootstrap method to choose the sample fraction in tail index estimation
Journal of Multivariate Analysis
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
Penalty and Barrier Methods: A Unified Framework
SIAM Journal on Optimization
Power-Law Distributions in Empirical Data
SIAM Review
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This paper studies the application of extreme value statistics (EVS) theory on analysis for stock data, based on interior penalty function algorithm and Bootstrap methods. The generalized Pareto distribution (GPD) models are considered in analyzing the closing price data of Shanghai stock market. The maximum likelihood estimates (MLEs) are obtained by using the interior penalty function algorithm. Correspondingly, the bias and standard errors of MLEs, and the hypothesis test on the shape parameter are concerned through Bootstrap methods. Some simulations are performed to demonstrate the efficacy of parameter estimation and the power of the test. The estimates of the tail index in this paper are compared with those obtained via classical methods. At last, the model is diagnosed by numerical and graphical methods and the Value-at-Risk (VaR) is estimated.