Initialement, la théorie du risque supposait l’indépendance entre les différentes variables aléatoires et autres paramètres intervenant dans la modélisation actuarielle. De nos jours, cette hypothèse d’indépendance est souvent relâchée afin de tenir compte de possibles interactions entre les différents éléments des modèles. Dans cette thèse, nous proposons d’introduire des modèles de dépendance pour différents aspects de la théorie du risque. Dans un premier temps, nous suggérons l’emploi des copules comme structure de dépendance. Nous abordons tout d’abord un problème d’allocation de capital basée sur la Tail-Value-at-Risk pour lequel nous supposons un lien introduit par une copule entre les différents risques. Nous obtenons des formules explicites pour le capital à allouer à l’ensemble du portefeuille ainsi que la contribution de chacun des risques lorsque nous utilisons la copule Farlie-Gumbel-Morgenstern. Pour les autres copules, nous fournissons une méthode d’approximation. Au deuxième chapitre, nous considérons le processus aléatoire de la somme des valeurs présentes des sinistres pour lequel les variables aléatoires du montant d’un sinistre et de temps écoulé depuis le sinistre précédent sont liées par une copule Farlie-Gumbel-Morgenstern. Nous montrons comment obtenir des formes explicites pour les deux premiers moments puis le moment d’ordre m de ce processus. Le troisième chapitre suppose un autre type de dépendance causée par un environnement extérieur. Dans le contexte de l’étude de la probabilité de ruine d’une compagnie de réassurance, nous utilisons un environnement markovien pour modéliser les cycles de souscription. Nous supposons en premier lieu des temps de changement de phases de cycle déterministes puis nous les considérons ensuite influencés en retour par les montants des sinistres. Nous obtenons, à l’aide de la méthode d’erlangisation, une approximation de la probabilité de ruine en temps fini. / Initially, it was supposed in risk theory that the random variables and other parameters of actuarial models were independent. Nowadays, this hypothesis is often relaxed to take into account possible interactions. In this thesis, we propose to introduce some dependence models for different aspects of risk theory. In a first part, we use copulas as dependence structure. We first tackle a problem of capital allocation based on the Tail-Value-at-Risk where the risks are supposed to be dependent according to a copula. We obtain explicit formulas for the capital to be allocated to the overall portfolio but also for the contribution of each risk when we use a Farlie-Gumbel-Morenstern copula. For the other copulas, we give an approximation method. In the second chapter, we consider the stochastic process of the discounted aggregate claims where the random variables for the claim amount and the time since the last claim are linked by a Farlie-Gumbel-Morgenstern copula. We show how to obtain exact expressions for the first two moments and for the moment of order m of the process. The third chapter assumes another type of dependence that is caused by an external environment. In the context of the study of the ruin probability for a reinsurance company, we use a Markovian environment to model the underwriting cycles. We suppose first deterministic cycle phase changes and then that these changes can also be influenced by the claim amounts. We use the erlangization method to obtain an approximation for the finite time ruin probability.

[pt] O objetivo desta tese é apresentar novas alternativas para modelagem de variáveis aleatórias no setor de seguros, utilizando o arcabouço dos modelos orientados por score com parâmetros variantes no tempo. No primeiro artigo, propomos um modelo dinâmico para a distribuição do sinistro agregado, que corresponde à soma aleatória dos valores de sinistros (severidade) em determinado período de tempo. A obtenção da distribuição do sinistro agregado é um problema clássico na teoria do risco e fundamental para precificação de seguros, cálculo de provisões e de probabilidade de ruína. No entanto, a obtenção da expressão analítica para essa distribuição de probabilidade é uma tarefa difícil. Neste trabalho, especificamos distribuições não-Gaussianas, tanto para o número de sinistros como para severidade, sob o arcabouço GAS (Generalized Autoregressive Score), e, por meio do uso da Transformada Rápida de Fourier obtemos, numericamente, a distribuição do sinistro agregado. O segundo artigo trata da incorporação do efeito de variáveis macroeconômicas na modelagem de variáveis relevantes no setor de seguros, em linha com requisito internacional de avaliação de provisões de forma consistente com mercado, a qual leva em consideração as informações disponíveis nos mercados financeiros e de capital relevantes, utilizando metodologias e parâmetros consistentes com esses mercados. Modelamos uma série bivariada de número de sinistros (duas linhas de negócios) de seguros financeiros com modelos autorregressivos e utilizamos cópulas para modelar a estrutura de dependência das séries temporais condicionado aos modelos ajustados nas marginais. Com esta abordagem, é possível simular números de sinistros futuros de mais de uma carteira, podendo esse resultado ser utilizado em uma avaliação consistente de provisões e da saúde financeira da seguradora. / [en] The objective of this thesis is to present new alternatives for modeling random variables in the insurance industry, using the framework of the score driven models with time-varying parameters. In the first paper, we propose a dynamic model for the aggregate claims distribution, which corresponds to a random sum of claims severity in a certain period of time. Obtaining the aggregate claims distribution is a classic problem in the Risk Theory and fundamental for premium estimation, measurement of obligations and ruin probability valuation. However, obtaining the analytic expression for this probability distribution is a hard task. In this work, we specify nonGaussian distributions for both the number of claims and for the claims severity, under the GAS framework, and, through the use of the fast Fourier transform, we obtain, numerically, the aggregate claims distribution. The second paper deals with the incorporation of macroeconomic variables on the modeling of relevant variables in the insurance sector, in line with the international requirements for market consistent valuation of insurance liabilities, which means that one should take into account the available information in relevant financial and capital markets, using methodologies and parameters consistent with these markets. We model a bivariate time series (two lines of business) of financial insurance with autoregressive models and use copulas models to consider the dependency structure of the time series conditioned to the fitted models for the marginals. Within this approach, it is possible to simulate the numbers of claims from more than one portfolio, and this result can be used in a consistent valuation of liabilities and of the financial health of an insurer.