Some questions in risk management and high-dimensional data analysis

Empirical likelihood;Hypothesis testing;High-dimensional data;Risk measures;Copulas

Wang, Ruodu ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Empirical likelihood;    Hypothesis testing;    High-dimensional data;    Risk measures;    Copulas;   

Others  :  https://smartech.gatech.edu/bitstream/1853/44706/1/wang_ruodu_201208_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

This thesis addresses three topics in the area of statistics andprobability, with applications in risk management. First, for thetesting problems in the high-dimensional (HD) data analysis, wepresent a novel method to formulate empirical likelihood tests andjackknife empirical likelihood tests by splitting the sample intosubgroups. New tests are constructed to test the equality of two HDmeans, the coefficient in the HD linear models and the HD covariancematrices. Second, we propose jackknife empirical likelihood methodsto formulate interval estimations for important quantities inactuarial science and risk management, such as the risk-distortionmeasures, Spearman's rho and parametric copulas. Lastly, weintroduce the theory of completely mixable (CM) distributions. Wegive properties of the CM distributions, show that a few classes ofdistributions are CM and use the new technique to find the boundsfor the sum of individual risks with given marginal distributionsbut unspecific dependence structure. The result partially solves aproblem that had been a challenge for decades, and directly leads tothe bounds on quantities of interest in risk management, such as thevariance, the stop-loss premium, the price of the European optionsand the Value-at-Risk associated with a joint portfolio.