Dependency modeling and multidimensional risk measures.

Summary The purpose of this thesis is to develop some aspects of dependency modeling in risk management in dimension greater than one. The first chapter is a general introduction. The second chapter is an article entitled "Estimating Bivariate Tail: a copula based approach", submitted for publication. It concerns the construction of an estimator of the tail of a bivariate distribution. The construction of this estimator is based on a Peaks Over Threshold method and thus on a bivariate version of the Pickands-Balkema-de Haan Theorem. The modeling of the dependence is obtained via the Upper Tail Dependence Copula. We demonstrate convergence properties for the estimator thus constructed. The third chapter is based on a paper: "A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation", submitted for publication. We address the problem of extending classical risk measures, such as Value-at-Risk and Conditional-Tail-Expectation, in a multidimensional setting using the multivariate Kendall function. Finally, in the fourth chapter of the thesis, we propose a contour estimator of a bivariate distribution function with a plug-in method. We demonstrate convergence properties for the estimators thus constructed. This chapter of the thesis is also constituted by an article, entitled "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory", accepted for publication in the journal ESAIM:Probability and Statistics.