Dependence structures and limiting restults, with applications in finance and insurance.

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Charpentier, Arthur (2006) Dependence structures and limiting restults, with applications in finance and insurance. Doctorat Mathématiques, Faculteit Wetenschappen (Sciences), ENSAE ISBN 90-8649-039-5.

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Licence: Copyright All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm, electronic or any other means without written permission from the publisher. ISBN [90-8649-039-5 ] D/ [D/2006/10.705/36]

Autres Localisations: http://www.crest.fr/pageperso/lcharpent/charpent.htm, http://tel.archives-ouvertes.fr/index.php?halsid=9aa3ac7459f97fadb36cffcbf2b4800e&view_this_doc=tel-00082892&version=1

Résumé

This thesis focuses on limiting theorems for copulae. The first chapter is a survey on dependence and standard results on copulae, with applications in finance and insurance. The second chapter studies changes of the dependence structure in survival models, and obtains limiting results using a bivariate concept of directional regular variation in high dimensions. Using some fixed point theorems, invariant copulae are exhibited. Further, it is proven that Clayton's copula is the only one invariant by truncature. In chapter 3-5 is studied the particular case of Archimedean copulae.
Study in upper and lower is conducted, and limiting theorems are obtained. Chapter 6 tries to link standard approach in extreme values, and the one presented here, based on conditional copulae, i.e. obtained with joint exceedances. Chapter 7 focuses on nonparametric (kernel based) estimates of copula densities, using the transformed kernel approach, and beta kernels. And finally, a final chapter (a bijgevoegde stelling) focuses on temporal dependencies for natural events, and studies the notion of return period when observations are not independence. Some applications are considered, on windstorms and heat waves (using GARMA processes, with long memory) and on flood events using extension of ACD models, introduced for high frequency financial data.

Table des Matières

Introduction et principaux résultats
1 Modeling dependent risks using copulae
2 Dynamic models for credit risk
3 Lower tails for Archimedean copulae
4 Dynamic dependence ordering
5 Upper tails for Archimedean copulae
6 Extreme and copae
7 Nonparametric estimation of copulae density
8 Temporal depdencies for natural events

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