Show simple item record

dc.contributor.advisorYu, Xingxing
dc.contributor.authorHou, Yanxi
dc.date.accessioned2017-08-17T18:58:10Z
dc.date.available2017-08-17T18:58:10Z
dc.date.created2017-08
dc.date.issued2017-05-03
dc.date.submittedAugust 2017
dc.identifier.urihttp://hdl.handle.net/1853/58629
dc.description.abstractRecently, many risk measures have been developed for various types of risk based on multiple financial variables. However, statistical properties of these risk measures are not fully understood, and there are very few effective inference methods for them in applications to financial data. This thesis addresses asymptotic behaviors and statistical inference methods for several newly proposed risk measures, including relative risk and conditional value-at-risk. These risk metrics are intended to measure the tail risks and/or systemic risk in financial markets. We consider conditional Value-at-Risk based on a linear regression model. We extend the assumptions on predictors and errors of the model, which make the model more flexible for the financial data. We then consider a relative risk measure based on a benchmark variable. The relative risk measure is proposed as a monitoring index for systemic risk of financial system. We also propose a new tail dependence measure based on the limit of conditional Kendall’s tau. The new tail dependence can be used to distinguish between the asymptotic independence and dependence in extreme value theory. For asymptotic results of these measures, we derive both normal and Chi-squared approximations. These approximations are a basis for inference methods. For normal approximation, the asymptotic variances are too complicated to estimate due to the complex forms of risk measures. Quantifying uncertainty is a practical and important issue in risk management. We propose several empirical likelihood methods to construct interval estimation based on Chi-squared approximation. Simulation study and real data analysis illustrate the usefulness of these risk measures and our inference methods. In particular, the empirical likelihood methods are very effective and easy to implement for practical applications.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectEmpirical likelihood method
dc.subjectConditional value-at-risk
dc.subjectRelative risk
dc.subjectTail dependence
dc.subjectCopula
dc.subjectExtreme value theory
dc.titleStatistical inference for some risk measures
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberPeng, Liang
dc.contributor.committeeMemberZhilova, Mayya
dc.contributor.committeeMemberLivshyts, Galyna
dc.contributor.committeeMemberPopescu, Ionel
dc.date.updated2017-08-17T18:58:11Z


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record