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Title: Bayesian mixture models in extreme value theory with an application to investent portfolio analysis
Author: Ortiz Barranos, Antonio A.
Awarding Body: University of Kent
Current Institution: University of Kent
Date of Award: 2012
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In general terms, extreme events can be interpreted as: catastrophes, disasters, crisis, and crashes. For the purposes of this thesis, an extreme event can be defined as an event that has a small chance of occurrence, but has a high impact on the phenomenon in study. The number of fields where there is an interest in the study of extremes is quite extensive: hydrology, seismology, climatology, economics, insurance, finance, epidemiology, medicine, and even in sports science. Let us take the example of flooding. A common problem is to propose the height of a river barrier, such that it is feasible to build and it is unlikely to be breached. A useful way to approach this issue is to build the barrier up to a level, which is expected to be breached once every hundred years, for example. But to know what height this is, one needs to study extreme data. Similar examples or motivations can be posed for each of the fields listed. In the thesis, we focus on financial extremes, keeping in mind the following questions: what is an extreme?, how likely is it to occur?, what would be the impact of its occurrence?, and what can be done with this information? The case of the univariate framework has been developed quite extensively in the last 50 years. The aim of this work is to model multivariate behaviors of extremes. Multivariate extremes is a relatively new area and as such, it is still in development. Beside, the theory states that, unlike the univariate framework, there is not a unique parametric family of multivariate extreme distributions. An important part of a multivariate model is the dependence structure. The selection of the parametric form will determine the dependence structure, and in most of the cases, it is a rigid structure, in the sense that it hardly embraces different types of dependence among the variables.
Supervisor: Walker, Stephen G. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: QA Mathematics (inc Computing science)