Some questions in risk management and high-dimensional data analysis
Author(s)
Wang, Ruodu
Advisor(s)
Peng, Liang
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Abstract
This thesis addresses three topics in the area of statistics and
probability, with applications in risk management. First, for the
testing problems in the high-dimensional (HD) data analysis, we
present a novel method to formulate empirical likelihood tests and
jackknife empirical likelihood tests by splitting the sample into
subgroups. New tests are constructed to test the equality of two HD
means, the coefficient in the HD linear models and the HD covariance
matrices. Second, we propose jackknife empirical likelihood methods
to formulate interval estimations for important quantities in
actuarial science and risk management, such as the risk-distortion
measures, Spearman's rho and parametric copulas. Lastly, we
introduce the theory of completely mixable (CM) distributions. We
give properties of the CM distributions, show that a few classes of
distributions are CM and use the new technique to find the bounds
for the sum of individual risks with given marginal distributions
but unspecific dependence structure. The result partially solves a
problem that had been a challenge for decades, and directly leads to
the bounds on quantities of interest in risk management, such as the
variance, the stop-loss premium, the price of the European options
and the Value-at-Risk associated with a joint portfolio.
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Date
2012-05-04
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Text
Resource Subtype
Dissertation