Dependency structures and boundary results with applications to insurance finance.

Summary This thesis focuses on bounding theorems for copulae. The first chapter is a survey of dependence and standard results on copulae, with applications to finance and insurance. The second chapter studies changes in the dependence structure in survival models and obtains limiting results using a bivariate concept of regular directional variation in high dimensions. Using some fixed point theorems, invariant copulae is exposed. Further on, it is proved that the Clayton copula is the only one invariant by truncation. In chapter 3-5 is studied the particular case of Archimedean copulae. The study in upper and lower is conducted and the restriction theorems are obtained. Chapter 6 tries to link the standard approach in extreme values and the one presented here, based on conditional copulae, i.e. obtained with joint exceedances. Chapter 7 focuses nonparametric (kernel based) on copula density evaluations, 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 where the observations are not independent. We consider some applications, on storm winds and heat waves (using GARMA processes, with long memory) and on flood events using the extension of ACD models, presented for high frequency financial data.