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Structures de dépendance et résultats limites avec applications en finance assurance

Abstract : 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-
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Submitted on : Tuesday, November 7, 2006 - 8:00:00 AM
Last modification on : Friday, August 5, 2022 - 2:49:41 PM
Long-term archiving on: : Thursday, September 30, 2010 - 7:52:18 PM


  • HAL Id : pastel-00001990, version 1



Arthur Charpentier. Structures de dépendance et résultats limites avec applications en finance assurance. Mathématiques [math]. ENSAE ParisTech, 2006. Français. ⟨pastel-00001990⟩



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