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The US sub-prime mortgage crisis greatly affected not only the US economy but also other countries in the world. This thesis employs the extreme value theory and Value at Risk (VaR) analysis to assess the impact of the US sub-prime mortgage crisis on various stock markets of the MSCI indexes, including 10 countries and 7 areas. It is reasonable to guess that VaR value should increase after the crisis. The empirical analyses on these indexes conclude that (1) the American market indexes not only do not agree with the guess after the crisis but four American indexes are identical; (2) not all the Asia market indexes consist with the guess; (3) the European market indexes agree with the guess; (4) MSCI AC PACIFIC, NEW ZEALAND, and AUSTRALIA consist with the guess; (5) the behavior for the positive log returns is different from that for the negative returns in some MSCI indexes. Over speaking, the impacts of US sub-prime mortgage crisis on those countries are not the same.

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant « Estimating Bivariate Tail : a copula based approach », soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: « A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation», soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant « Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory», accepté pour publication dans la revue ESAIM:Probability and Statistics. / In this PhD thesis we consider different aspects of dependence modeling with applications in multivariate risk theory. The first chapter is constituted by a general introduction. The second chapter is essentially constituted by the article “Estimating Bivariate Tail: a copula based approach”, actually submitted for publication. It deals with the problem of estimating the tail of a bivariate distribution function. We develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. The dependence structure between the marginals in the upper tails is described by the Upper Tail Dependence Copula. Then we construct a two-dimensional tail estimator and study its asymptotic properties. The third chapter of this thesis is based on the article “A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation” and submitted for publication. We propose a multivariate generalization of risk measures as Value-at-Risk and Conditional-Tail-Expectation and we analyze the behavior of these measures in terms of classical properties of risk measures. We study the behavior of these measures with respect to different risk scenarios and stochastic ordering of marginals risks. Finally in the fourth chapter we introduce a consistent procedure to estimate level sets of an unknown bivariate distribution function, using a plug-in approach in a non-compact setting. Also this chapter is constituted by the article “Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory”, accepted for publication in ESAIM: Probability and Statistics journal.

The main objective of wave energy converters (WECs) is to ensure reliable electricity production at a competitive cost. Two challenges to achieving this are ensuring an efficient energy conversion and offshore survivability.         This thesis work is structured in three different sections: Control and maximum power optimization, forces and dynamics analysis in extreme wave conditions, and statistical modeling of extreme loads in reliability analysis.        The need for prediction and future knowledge of waves and wave forces is essential due to the non-causality of the optimal velocity relation for wave energy converters. Using generic concepts and modes of motion, the sensitivity of the prediction horizon to various parameters encountered in a real system is elaborated. The results show that through a realistic assumption of the dissipative losses, only a few seconds to about half a wave cycle is sufficient to predict the required future knowledge for the aim of maximizing the power absorption.          The results of a 1:30 scaled wave tank experiment are used to assess the line force and dynamic behaviour of a WEC during extreme wave events. Within the comparison of different wave type representations, i.e. irregular, regular and focused waves, of the same sea state, the results show that not all the wave types deliver the same maximum line forces. As a strategy of mitigating the line forces during extreme wave events, changing the power take-off (PTO) damping may be employed. With consideration of the whole PTO range, the results indicate an optimum damping value for each sea state in which the smallest maximum line force is obtained. Although wave breaking slamming and end-stop spring compression lead to high peak line forces, it is possible that they level out due to the overtopping effect. Waves with a long wavelength result in large surge motion and consequently higher and more damaging forces.         On the investigation of reliability assessment of the wave energy converter systems, computing the return period of the extreme forces is crucial. Using force measurement force data gathered at the west coast of Sweden, the extreme forces are statistically modelled with the peak-over-threshold method. Then, the return level of the extreme forces over 20 years for the calm season of the year is computed.