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Theses

Dépendance et résultats limites, quelques applications en finance et assurance

Abstract : This thesis focuses on risk dependencies, based on copula functions. Taking dependencies into account is now crucial in risk management, since amount can be huge (contagion risk and domino effect in credit risk, or correlation of extremal risks in reinsurance).
Hence, a better knowledge of dependencies a therefore a key issue, and thus fundamental properties are needed. The goal of this thesis is then to focus on changes of the dependence structure: change in time (in finance) or change in tails (in reinsurance).

The first part is based on the dynamic approach in credit risk model, and change in time of the survival copula. Introducing conditional copula, it will be possible to study dependencies among time before defaults of bonds, given that no default has been observe on a given period of time. Some fixed point theorem have been derived to obtain limiting behaviors, and then price first-to-default contracts.

The following chapter study the use of conditional copulas when modeling extreme risks. Multivariate extreme value theory has been developed using a maximum componentwise approach. But extremal events definded as joint exceedences actually offers wider results. More precisely, the study of lower and upper tails will be presented in the Archimedean case, focusing on the definition of tail independence. And finally, two extentions of Pickands-Balkema-de Haan theorem in dimension 2 will be given.

The final part is based on nonparametric estimation of copula densities, where some kernel based estimates are considered, and some correction are proposed to avoid multiplicative bias in corners (tail dependence). Note that some techniques are also proposed to drop censuring bias.

And finally, a bijgevoegde stelling concludes the thesis, study temporal dependencies in environmental risks. Hence, long-memory models are considered, to model storms and probability of occurrence of consecutive storms (as in December 1999), and then to get an accurate estimate for the return period of 2003's heat wave.
Finally, some high-frequency models (as the one introduced in finance) are considered to model hydrological series, and get new estimates for flood risk.
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https://tel.archives-ouvertes.fr/tel-00082892
Contributor : Arthur Charpentier <>
Submitted on : Thursday, June 29, 2006 - 7:37:22 AM
Last modification on : Monday, October 19, 2020 - 10:58:50 AM
Long-term archiving on: : Tuesday, September 18, 2012 - 3:20:14 PM

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Arthur Charpentier. Dépendance et résultats limites, quelques applications en finance et assurance. Mathématiques [math]. Université Catholique de Louvain, 2006. Français. ⟨tel-00082892⟩

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