Date of Award
2007
Degree Type
Thesis
Degree Name
Doctor of Philosophy
Program
Design and Manufacturing Engineering
Supervisor
Dr. Bruce Jones
Abstract
During the past few decades there has been an extensive amount of work involving the modelling of extreme events. A reasonably accurate estimate of the probabilities associated with these events contributes to a good understanding of the risk taken. Extreme Value Theory provides powerful tools to aid in investigating this risk.
In applications involving more than one random variable of interest, it is neces sary to understand the extremal behaviour of the dependence structure as well as the extremal behaviour of the marginal distributions. In this thesis, the focus is on ex plaining the extremal dependence structure and its impact on financial and actuarial applications.
The first two contributions of this thesis are mainly focused on the extreme be haviour of two commonly used classes of multivariate distributions in finance and insurance, namely phase-type and elliptical. In the phase-type case, we examine the limiting distributions of the componentwise maxima and minima, while asymptotic results are obtained for joint threshold exceedance probabilities in the elliptical case.
The next two contributions present asymptotic results for large claims reinsurance. Specifically, we focus on ECOMOR (excédent du coût moyen relatif) and LCR (largest claims reinsurance). We provide asymptotic tail probabilities that can be used to
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estimate certain risk measures, such as the Value-at-Risk. Two specific models are investigated; one represents the total claims under a claims process for which each claim amount depends on the time since the previous claim and the other represents the total claims under n dependent insurance contracts.
Recommended Citation
Asimit, Alexandru Valentin, "DEPENDENCE MODELLING OF EXTREME EVENTS WITH APPLICATIONS IN FINANCE AND INSURANCE" (2007). Digitized Theses. 4961.
https://ir.lib.uwo.ca/digitizedtheses/4961